{"id":122776,"date":"2022-02-20T14:44:01","date_gmt":"2022-02-20T09:14:01","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=122776"},"modified":"2024-04-09T14:26:05","modified_gmt":"2024-04-09T08:56:05","slug":"study-materials-ncert-exemplar-solutions-class-8-maths-chapter-7-algebraic-expressions-and-identities-factorisation","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/","title":{"rendered":"NCERT Exemplar Solutions Class 8 Maths Solutions Chapter 7 Algebraic Expression, Identities &#038; Factorisation"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#NCERT_Exemplar_Solutions_Class_8_Maths_Solutions_Chapter_7_Algebraic_Expression_Identities_Factorization\" title=\"NCERT Exemplar Solutions Class 8 Maths Solutions Chapter 7 Algebraic Expression, Identities &amp; Factorization\">NCERT Exemplar Solutions Class 8 Maths Solutions Chapter 7 Algebraic Expression, Identities &amp; Factorization<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#Class_8_Maths_Chapter_7_FAQs\" title=\"Class 8 Maths Chapter 7 FAQs\">Class 8 Maths Chapter 7 FAQs<\/a><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><ul class='ez-toc-list-level-5'><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#What_kind_of_questions_are_there_in_these_NCERT_Exemplar_Solutions\" title=\"What kind of questions are there in these NCERT Exemplar Solutions?\">What kind of questions are there in these NCERT Exemplar Solutions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#Is_NCERT_Exemplar_Solutions_of_this_Chapter_enough_to_attend_all_the_questions_that_come_in_the_board_exam\" title=\"Is NCERT Exemplar Solutions of this Chapter enough to attend all the questions that come in the board exam?\">Is NCERT Exemplar Solutions of this Chapter enough to attend all the questions that come in the board exam?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#Is_it_necessary_to_learn_all_the_topics_provided_in_NCERT_Exemplar_Solutions_for_Class_8_Maths_Chapter_7\" title=\"Is it necessary to learn all the topics provided in NCERT Exemplar Solutions for Class 8 Maths Chapter 7?\">Is it necessary to learn all the topics provided in NCERT Exemplar Solutions for Class 8 Maths Chapter 7?<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Exemplar_Solutions_Class_8_Maths_Solutions_Chapter_7_Algebraic_Expression_Identities_Factorization\"><\/span>NCERT Exemplar Solutions Class 8 Maths Solutions Chapter 7 Algebraic Expression, Identities &amp; Factorization<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Subject specialists have designed <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/\"><strong>NCERT Exemplar Solutions for Maths Class 8<\/strong><\/a> Chapter 7 which includes thorough solutions for reference. These solutions are updated according to the latest <a href=\"https:\/\/infinitylearn.com\/surge\/cbse\/cbse-syllabus\/\"><strong>CBSE syllabus<\/strong><\/a> for 2024-25 and are provided in easy language for understanding. Tips and tricks are also provided. These solutions are provided so a student can clear his doubts and get help with a deep understanding of the concept. Also, you can refer them to make the chapter notes and revisions notes. PDF of this can also be downloaded from the website.<\/p>\n<ol>\n<li><strong> The product of a monomial and a binomial is a<\/strong><\/li>\n<\/ol>\n<p><strong>(a) monomial (b) binomial<\/strong><\/p>\n<p><strong>(c) trinomial (d) none of these<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) binomial<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The product of a monomial and a binomial results in a <\/span><strong>binomial<\/strong><span style=\"font-weight: 400;\">. Let&#8217;s consider a monomial as 2x and a binomial as x + y. The product of a monomial and a binomial is calculated as (2x) \u00d7 (x + y) This simplifies to 2x^2 + 2xy.<\/span><\/p>\n<ol start=\"2\">\n<li><strong> In a polynomial, the exponents of the variables are always<\/strong><\/li>\n<\/ol>\n<p><strong>(a) integers (b) positive integers<\/strong><\/p>\n<p><strong>(c) non-negative integers (d) non-positive integers<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) positive integers<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In a polynomial, the exponents of the variables are always <\/span><strong>positive integers<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"3\">\n<li><strong> Which of the following is correct?<\/strong><\/li>\n<\/ol>\n<p><strong>(a) (a \u2013 b)<\/strong><strong>2<\/strong><strong> = a<\/strong><strong>2<\/strong><strong> + 2ab \u2013 b<\/strong><strong>2<\/strong><strong> (b) (a \u2013 b)<\/strong><strong>2<\/strong><strong> = a<\/strong><strong>2<\/strong><strong> \u2013 2ab + b<\/strong><strong>2<\/strong><\/p>\n<p><strong>(c) (a \u2013 b)<\/strong><strong>2<\/strong><strong> = a<\/strong><strong>2<\/strong><strong> \u2013 b<\/strong><strong>2<\/strong><strong> (d) (a + b)<\/strong><strong>2<\/strong><strong> = a<\/strong><strong>2<\/strong><strong> + 2ab \u2013 b<\/strong><strong>2<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) (a \u2013 b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab + b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We have, = (a \u2013 b) \u00d7 (a \u2013 b)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a \u00d7 (a \u2013 b) \u2013 b \u00d7 (a \u2013 b)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 ab \u2013 ba + b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab + b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The correct expansion for (a &#8211; b)^2 is a^2 &#8211; 2ab + b^2.<\/span><\/p>\n<ol start=\"4\">\n<li><strong> The sum of \u20137pq and 2pq is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) \u20139pq (b) 9pq (c) 5pq (d) \u2013 5pq<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(d) \u2013 5pq<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The sum of -7pq and 2pq is <\/span><strong>-5pq<\/strong><span style=\"font-weight: 400;\"> as they are like terms.<\/span><\/p>\n<ol start=\"5\">\n<li><strong> If we subtract \u20133x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong> from x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong>, then we get<\/strong><\/li>\n<\/ol>\n<p><strong>(a) \u2013 4x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong> (b) \u2013 2x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong> (c) 2x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong> (d) 4x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(d) 4x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Subtracting -3x^2y^2 from x^2y^2 results in 4x^2y^2.<\/span><\/p>\n<ol start=\"6\">\n<li><strong> Like term as 4m<\/strong><strong>3<\/strong><strong>n<\/strong><strong>2<\/strong><strong> is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 4m<\/strong><strong>2<\/strong><strong>n<\/strong><strong>2<\/strong><strong> (b) \u2013 6m<\/strong><strong>3<\/strong><strong>n<\/strong><strong>2<\/strong><strong> (c) 6pm<\/strong><strong>3<\/strong><strong>n<\/strong><strong>2<\/strong><strong> (d) 4m<\/strong><strong>3<\/strong><strong>n<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) \u2013 6m<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A like term to 4m^3n^2 is <\/span><strong>-6m^3n^2<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"7\">\n<li><strong> Which of the following is a binomial?<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 7 \u00d7 a + a (b) 6a<\/strong><strong>2<\/strong><strong> + 7b + 2c<\/strong><\/p>\n<p><strong>(c) 4a \u00d7 3b \u00d7 2c (d) 6 (a<\/strong><strong>2<\/strong><strong> + b)<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(d) 6 (a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">A binomial among the options is <\/span><strong>6(a^2 + b)<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"8\">\n<li><strong> Sum of a \u2013 b + ab, b + c \u2013 bc and c \u2013 a \u2013 ac is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 2c + ab \u2013 ac \u2013 bc (b) 2c \u2013 ab \u2013 ac \u2013 bc<\/strong><\/p>\n<p><strong>(c) 2c + ab + ac + bc (d) 2c \u2013 ab + ac + bc<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a) 2c + ab \u2013 ac \u2013 bc<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The sum of a &#8211; b + ab, b + c &#8211; bc, and c &#8211; a &#8211; ac simplifies to <\/span><strong>2c + ab &#8211; ac &#8211; bc<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"9\">\n<li><strong> Product of the following monomials 4p, \u2013 7q<\/strong><strong>3<\/strong><strong>, \u20137pq is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 196 p<\/strong><strong>2<\/strong><strong>q<\/strong><strong>4<\/strong><strong> (b) 196 pq<\/strong><strong>4<\/strong><strong> (c) \u2013 196 p<\/strong><strong>2<\/strong><strong>q<\/strong><strong>4<\/strong><strong> (d) 196 p<\/strong><strong>2<\/strong><strong>q<\/strong><strong>3<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a) 196 p<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">q<\/span><span style=\"font-weight: 400;\">4<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The product of 4p, -7q^3, and -7pq is 196p^2q^4.<\/span><\/p>\n<ol start=\"10\">\n<li><strong> Area of a rectangle with length 4ab and breadth 6b<\/strong><strong>2<\/strong><strong> is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 24a<\/strong><strong>2<\/strong><strong>b<\/strong><strong>2<\/strong><strong> (b) 24ab<\/strong><strong>3<\/strong><strong> (c) 24ab<\/strong><strong>2<\/strong><strong> (d) 24ab<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) 24ab<\/span><span style=\"font-weight: 400;\">3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The area of a rectangle with length 4ab and breadth 6b^2 is <\/span><strong>24ab^3<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"11\">\n<li><strong> Volume of a rectangular box (cuboid) with length = 2ab, breadth = 3ac and height = 2ac is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 12a<\/strong><strong>3<\/strong><strong>bc<\/strong><strong>2<\/strong><strong> (b) 12a<\/strong><strong>3<\/strong><strong>bc (c) 12a<\/strong><strong>2<\/strong><strong>bc (d) 2ab +3ac + 2ac<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a) 12a<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">bc<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The volume of a rectangular box with dimensions 2ab, 3ac, and 2ac is <\/span><strong>12a^3bc^2<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"12\">\n<li><strong> Product of 6a<\/strong><strong>2<\/strong><strong> \u2013 7b + 5ab and 2ab is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 12a<\/strong><strong>3<\/strong><strong>b \u2013 14ab<\/strong><strong>2<\/strong><strong> + 10ab (b) 12a<\/strong><strong>3<\/strong><strong>b \u2013 14ab<\/strong><strong>2<\/strong><strong> + 10a<\/strong><strong>2<\/strong><strong>b<\/strong><strong>2<\/strong><\/p>\n<p><strong>(c) 6a<\/strong><strong>2<\/strong><strong> \u2013 7b + 7ab (d) 12a<\/strong><strong>2<\/strong><strong>b \u2013 7ab<\/strong><strong>2<\/strong><strong> + 10ab<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) 12a<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">b \u2013 14ab<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 10a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The product of 6a^2 &#8211; 7b + 5ab and 2ab simplifies to <\/span><strong>12a^3b &#8211; 14ab^2 + 10a^2b^2<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"13\">\n<li><strong> Square of 3x \u2013 4y is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 9x<\/strong><strong>2<\/strong><strong> \u2013 16y<\/strong><strong>2<\/strong><strong> (b) 6x<\/strong><strong>2<\/strong><strong> \u2013 8y<\/strong><strong>2<\/strong><\/p>\n<p><strong>(c) 9x<\/strong><strong>2<\/strong><strong> + 16y<\/strong><strong>2<\/strong><strong> + 24xy (d) 9x<\/strong><strong>2<\/strong><strong> + 16y<\/strong><strong>2<\/strong><strong> \u2013 24xy<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(d) 9x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 16y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 24xy<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The square of 3x &#8211; 4y is <\/span><strong>9x^2 + 16y^2 &#8211; 24xy<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"14\">\n<li><strong> Which of the following are like terms?<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 5xyz<\/strong><strong>2<\/strong><strong>, \u2013 3xy<\/strong><strong>2<\/strong><strong>z (b) \u2013 5xyz<\/strong><strong>2<\/strong><strong>, 7xyz<\/strong><strong>2<\/strong><\/p>\n<p><strong>(c) 5xyz<\/strong><strong>2<\/strong><strong>, 5x<\/strong><strong>2<\/strong><strong>yz (d) 5xyz<\/strong><strong>2<\/strong><strong>, x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong>z<\/strong><strong>2<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) \u2013 5xyz<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">, 7xyz<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Like terms among the options are <\/span><strong>-5xyz^2, 7xyz^2<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"15\">\n<li><strong> Coefficient of y in the term \u2013y\/3 is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) \u2013 1 (b) \u2013 3 (c) -1\/3 (d) 1\/3<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(c) -1\/3<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The coefficient of y in the term -y\/3 is <\/span><strong>-1\/3.<\/strong><\/p>\n<ol start=\"16\">\n<li><strong> a<\/strong><strong>2<\/strong><strong> \u2013 b<\/strong><strong>2<\/strong><strong> is equal to<\/strong><\/li>\n<\/ol>\n<p><strong>(a) (a \u2013 b)<\/strong><strong>2<\/strong><strong> (b) (a \u2013 b) (a \u2013 b)<\/strong><\/p>\n<p><strong>(c) (a + b) (a \u2013 b) (d) (a + b) (a + b)<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(c) (a + b) (a \u2013 b)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The expression a^2 &#8211; b^2 is equal to <\/span><strong>(a + b)(a &#8211; b)<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"17\">\n<li><strong> Common factor of 17abc, 34ab<\/strong><strong>2<\/strong><strong>, 51a<\/strong><strong>2<\/strong><strong>b is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 17abc (b) 17ab (c) 17ac (d) 17a<\/strong><strong>2<\/strong><strong>b<\/strong><strong>2<\/strong><strong>c<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) 17ab<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The common factor of 17abc, 34ab^2, and 51a^2b is <\/span><strong>17ab<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"18\">\n<li><strong> Square of 9x \u2013 7xy is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 81x<\/strong><strong>2<\/strong><strong> + 49x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong> (b) 81x<\/strong><strong>2<\/strong><strong> \u2013 49x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><\/p>\n<p><strong>(c) 81x<\/strong><strong>2<\/strong><strong> + 49x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong> \u2013126x<\/strong><strong>2<\/strong><strong>y (d) 81x<\/strong><strong>2<\/strong><strong> + 49x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong> \u2013 63x<\/strong><strong>2<\/strong><strong>y<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(c) 81x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 49x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013126x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">y<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The square of 9x &#8211; 7xy simplifies to <\/span><strong>81x^2 + 49x^2y^2 &#8211; 126x^2y.<\/strong><\/p>\n<ol start=\"19\">\n<li><strong> Factorised form of 23xy \u2013 46x + 54y \u2013 108 is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) (23x + 54) (y \u2013 2) (b) (23x + 54y) (y \u2013 2)<\/strong><\/p>\n<p><strong>(c) (23xy + 54y) (\u2013 46x \u2013 108) (d) (23x + 54) (y + 2)<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a) (23x + 54) (y \u2013 2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The factorised form of 23xy &#8211; 46x + 54y &#8211; 108 is <\/span><strong>(23x + 54)(y &#8211; 2)<\/strong><\/p>\n<ol start=\"20\">\n<li><strong> Factorised form of r<\/strong><strong>2<\/strong><strong> \u2013 10r + 21 is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) (r \u2013 1) (r \u2013 4) (b) (r \u2013 7) (r \u2013 3)<\/strong><\/p>\n<p><strong>(c) (r \u2013 7) (r + 3) (d) (r + 7) (r + 3)<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) (r \u2013 7) (r \u2013 3)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The factorised form of r^2 &#8211; 10r + 21 is <\/span><strong>(r &#8211; 7)(r &#8211; 3)<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"21\">\n<li><strong> Factorised form of p<\/strong><strong>2<\/strong><strong> \u2013 17p \u2013 38 is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) (p \u2013 19) (p + 2) (b) (p \u2013 19) (p \u2013 2)<\/strong><\/p>\n<p><strong>(c) (p + 19) (p + 2) (d) (p + 19) (p \u2013 2)<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a) (p \u2013 19) (p + 2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The factorised form of p^2 &#8211; 17p &#8211; 38 is <\/span><strong>(p &#8211; 19)(p + 2)<\/strong><span style=\"font-weight: 400;\">.<\/span><\/p>\n<ol start=\"22\">\n<li><strong> On dividing 57p<\/strong><strong>2<\/strong><strong>qr by 114pq, we get<\/strong><\/li>\n<\/ol>\n<p><strong>(a) \u00bcpr (b) \u00bepr (c) \u00bdpr (d) 2pr<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(c) \u00bdpr<\/span><\/p>\n<p><span style=\"font-weight: 400;\">On dividing 57p<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">qr by 114pq,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">It can be expanded as = (57 \u00d7 p \u00d7 p \u00d7 q \u00d7 r)\/(114 \u00d7 p \u00d7 q)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 57pr\/114 \u2026 [divide both numerator and denominator by 57]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= \u00bdpr<\/span><\/p>\n<ol start=\"23\">\n<li><strong> On dividing p (4p<\/strong><strong>2<\/strong><strong> \u2013 16) by 4p (p \u2013 2), we get<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 2p + 4 (b) 2p \u2013 4 (c) p + 2 (d) p \u2013 2<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(c) p + 2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">On dividing p (4p<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 16) by 4p (p \u2013 2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (p((2p)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 (4)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">))\/ (4p(p \u2013 2))<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= ((2p \u2013 4) \u00d7 (2p + 4))\/(4(p \u2013 2))<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Take out the common factors<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= ((2(p \u2013 2)) \u00d7 (2 (p + 4)))\/(4(p -2))<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (4(p \u2013 2)(p + 2))\/ (4(p \u2013 2))<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= p + 2<\/span><\/p>\n<ol start=\"24\">\n<li><strong> The common factor of 3ab and 2cd is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 1 (b) \u2013 1 (c) a (d) c<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a) 1<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The common factor of 3ab and 2cd is 1, as there is no common factor except 1 between them.<\/span><\/p>\n<ol start=\"25\">\n<li><strong> An irreducible factor of 24x<\/strong><strong>2<\/strong><strong>y<\/strong><strong>2<\/strong><strong> is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) x<\/strong><strong>2<\/strong><strong> (b) y<\/strong><strong>2<\/strong><strong> (c) x (d) 24x<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(c) x<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The irreducible factor of 24x\u00b2y\u00b2 is x, as it cannot be further factored into simpler components.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">24x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">y<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 x \u00d7 x \u00d7 y \u00d7 y<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Therefore an irreducible factor is x.<\/span><\/p>\n<ol start=\"26\">\n<li><strong> Number of factors of (a + b)<\/strong><strong>2<\/strong><strong> is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 4 (b) 3 (c) 2 (d) 1<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(c) 2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The number of factors of (a + b)\u00b2 is 2, as further factorization is not possible beyond (a + b)(a + b).<\/span><\/p>\n<ol start=\"27\">\n<li><strong> The factorised form of 3x \u2013 24 is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 3x \u00d7 24 (b) 3 (x \u2013 8) (c) 24 (x \u2013 3) (d) 3(x \u2013 12)<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) 3 (x \u2013 8)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The factorised form of 3x &#8211; 24 is 3(x &#8211; 8), where 3 is taken out as a common factor.<\/span><\/p>\n<ol start=\"28\">\n<li><strong> The factors of x<\/strong><strong>2<\/strong><strong> \u2013 4 are<\/strong><\/li>\n<\/ol>\n<p><strong>(a) (x \u2013 2), (x \u2013 2) (b) (x + 2), (x \u2013 2)<\/strong><\/p>\n<p><strong>(c) (x + 2), (x + 2) (d) (x \u2013 4), (x \u2013 4)<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) (x + 2), (x \u2013 2)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The factors of x\u00b2 &#8211; 4 are (x + 2) and (x &#8211; 2), as x\u00b2 &#8211; 4 can be expressed as (x + 2)(x &#8211; 2).<\/span><\/p>\n<ol start=\"29\">\n<li><strong> The value of (\u2013 27x<\/strong><strong>2<\/strong><strong>y) \u00f7 (\u2013 9xy) is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 3xy (b) \u2013 3xy (c) \u2013 3x (d) 3x<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(d) 3x<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The value of (-27x\u00b2y) \u00f7 (-9xy) is 3x, obtained by simplifying the division.<\/span><\/p>\n<ol start=\"30\">\n<li><strong> The value of (2x<\/strong><strong>2<\/strong><strong> + 4) \u00f7 2 is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 2x<\/strong><strong>2<\/strong><strong> + 2 (b) x<\/strong><strong>2<\/strong><strong> + 2 (c) x<\/strong><strong>2<\/strong><strong> + 4 (d) 2x<\/strong><strong>2<\/strong><strong> + 4<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(b) x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The value of (2x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 4) \u00f7 2 = (2x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 4)\/2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (2(x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2))\/2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2<\/span><\/p>\n<ol start=\"31\">\n<li><strong> The value of (3x<\/strong><strong>3<\/strong><strong> +9x<\/strong><strong>2<\/strong><strong> + 27x) \u00f7 3x is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) x<\/strong><strong>2<\/strong><strong> +9 + 27x (b) 3x<\/strong><strong>3<\/strong><strong> +3x<\/strong><strong>2<\/strong><strong> + 27x<\/strong><\/p>\n<p><strong>(c) 3x<\/strong><strong>3<\/strong><strong> +9x<\/strong><strong>2<\/strong><strong> + 9 (d) x<\/strong><strong>2<\/strong><strong> +3x + 9<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(d) x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> +3x + 9<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The value of (3x<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> +9x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 27x) \u00f7 3x = (3x<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> + 9x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 27x)\/3x<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Takeout 3x as common,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 3x (x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 3x + 9)\/3x<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 3x + 9<\/span><\/p>\n<ol start=\"32\">\n<li><strong> The value of (a + b)<\/strong><strong>2<\/strong><strong> + (a \u2013 b)<\/strong><strong>2<\/strong><strong> is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 2a + 2b (b) 2a \u2013 2b (c) 2a<\/strong><strong>2<\/strong><strong> + 2b<\/strong><strong>2<\/strong><strong> (d) 2a<\/strong><strong>2<\/strong><strong> \u2013 2b<\/strong><strong>2<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(c) 2a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(a + b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + (a \u2013 b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = (a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2ab) + (a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">) + (b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">) + (2ab \u2013 2ab)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 2a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<ol start=\"33\">\n<li><strong> The value of (a + b)<\/strong><strong>2<\/strong><strong> \u2013 (a \u2013 b)<\/strong><strong>2<\/strong><strong> is<\/strong><\/li>\n<\/ol>\n<p><strong>(a) 4ab (b) \u2013 4ab (c) 2a<\/strong><strong>2<\/strong><strong> + 2b<\/strong><strong>2<\/strong><strong> (d) 2a<\/strong><strong>2<\/strong><strong> \u2013 2b<\/strong><strong>2<\/strong><\/p>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a) 4ab<\/span><\/p>\n<p><span style=\"font-weight: 400;\">The value of (a + b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 (a \u2013 b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = (a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2ab) \u2013 (a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2ab + 2ab<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 4ab<\/span><\/p>\n<p><strong>In questions 34 to 58, fill in the blanks to make the statements true:<\/strong><\/p>\n<ol start=\"34\">\n<li><strong> The product of two terms with like signs is a term.<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">The product of two terms with like signs is a positive term.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let us assume two like terms are, 3p and 2q<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 3p \u00d7 2q<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 6pq<\/span><\/p>\n<ol start=\"35\">\n<li><strong> The product of two terms with unlike signs is a term.<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">The product of two terms with unlike signs is a negative term.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Let us assume two unlike terms are, \u2013 3p and 2q<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= -3p \u00d7 2q<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= \u2013 6pq<\/span><\/p>\n<ol start=\"36\">\n<li><strong> a (b + c) = a \u00d7 ____ + a \u00d7 _____.<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">a (b + c) = a \u00d7 b + a \u00d7 c. \u2026 [by using left distributive law]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= ab + ac<\/span><\/p>\n<ol start=\"37\">\n<li><strong> (a \u2013 b) _________ = a<\/strong><strong>2<\/strong><strong> \u2013 2ab + b<\/strong><strong>2<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a \u2013 b) (a \u2013 b) = (a \u2013 b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab + b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">(a \u2013 b) (a \u2013 b)= a \u00d7 (a \u2013 b) \u2013 b \u00d7 (a \u2013 b)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 ab \u2013 ba + b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab + b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<ol start=\"38\">\n<li><strong> a<\/strong><strong>2<\/strong><strong> \u2013 b<\/strong><strong>2<\/strong><strong> = (a + b ) __________.<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = (a + b) (a \u2013 b) \u2026 [from the standard identities]<\/span><\/p>\n<ol start=\"39\">\n<li><strong> (a \u2013 b)<\/strong><strong>2<\/strong><strong> + ____________ = a<\/strong><strong>2<\/strong><strong> \u2013 b<\/strong><strong>2<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a \u2013 b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + (2ab \u2013 2b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">) = a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (a \u2013 b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + (2ab \u2013 2b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab + 2ab \u2013 2b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<ol start=\"40\">\n<li><strong> (a + b)<\/strong><strong>2<\/strong><strong> \u2013 2ab = ___________ + ____________<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(a + b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab = a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (a + b)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + 2ab + b<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> \u2013 2ab<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= a<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + b<\/span><span style=\"font-weight: 400;\">2<\/span><\/p>\n<ol start=\"41\">\n<li><strong> (x + a) (x + b) = x<\/strong><strong>2<\/strong><strong> + (a + b) x + ________.<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">(x + a) (x + b) = x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + (a + b) x + ab<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (x + a) (x + b)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= x \u00d7 (x + b) + a \u00d7 (x + b)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + xb + xa + ab<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + x (b + a) + ab<\/span><\/p>\n<ol start=\"42\">\n<li><strong> The product of two polynomials is a ________.<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">The product of two polynomials is a polynomial.<\/span><\/p>\n<ol start=\"43\">\n<li><strong> Common factor of ax<\/strong><strong>2<\/strong><strong> + bx is __________.<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">Common factor of ax<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> + bx is x (ax + b)<\/span><\/p>\n<ol start=\"44\">\n<li><strong> Factorised form of 18mn + 10mnp is ________.<\/strong><\/li>\n<\/ol>\n<p><strong>Solution:-<\/strong><\/p>\n<p><span style=\"font-weight: 400;\">Factorised form of 18mn + 10mnp is 2mn (9 + 5p)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= (2 \u00d7 9 \u00d7 m \u00d7 n) + (2 \u00d7 5 \u00d7 m \u00d7 n \u00d7 p)<\/span><\/p>\n<p><span style=\"font-weight: 400;\">= 2mn (9 + 5p)<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Class_8_Maths_Chapter_7_FAQs\"><\/span>Class 8 Maths Chapter 7 FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"What_kind_of_questions_are_there_in_these_NCERT_Exemplar_Solutions\"><\/span>What kind of questions are there in these NCERT Exemplar Solutions?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThis chapter deals with multiple choice questions, descriptive type of questions, long answer type questions, short answer type questions, fill in the blanks, and daily life examples. In end, students can increase their problem-solving skills also with time management skills. This will help you to score good marks\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Is_NCERT_Exemplar_Solutions_of_this_Chapter_enough_to_attend_all_the_questions_that_come_in_the_board_exam\"><\/span>Is NCERT Exemplar Solutions of this Chapter enough to attend all the questions that come in the board exam?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tYes, these NCERT Exemplar Solutions deal with solutions for all questions given in NCERT Textbook Maths for Class 8. Most of the questions coming in the exams are from these exercises. By studying these concepts, you can achieve good grades.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h5><span class=\"ez-toc-section\" id=\"Is_it_necessary_to_learn_all_the_topics_provided_in_NCERT_Exemplar_Solutions_for_Class_8_Maths_Chapter_7\"><\/span>Is it necessary to learn all the topics provided in NCERT Exemplar Solutions for Class 8 Maths Chapter 7?<span class=\"ez-toc-section-end\"><\/span><\/h5>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tYes. As these questions seem to be important for exams. These questions are solved by subject matter experts for helping students to crack these exercises easily. These solutions give students knowledge about data handling. Solutions can be downloaded in PDF format on the Infinity Learn website.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What kind of questions are there in these NCERT Exemplar Solutions?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"This chapter deals with multiple choice questions, descriptive type of questions, long answer type questions, short answer type questions, fill in the blanks, and daily life examples. In end, students can increase their problem-solving skills also with time management skills. This will help you to score good marks\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Is NCERT Exemplar Solutions of this Chapter enough to attend all the questions that come in the board exam?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Yes, these NCERT Exemplar Solutions deal with solutions for all questions given in NCERT Textbook Maths for Class 8. Most of the questions coming in the exams are from these exercises. By studying these concepts, you can achieve good grades.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Is it necessary to learn all the topics provided in NCERT Exemplar Solutions for Class 8 Maths Chapter 7?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Yes. As these questions seem to be important for exams. These questions are solved by subject matter experts for helping students to crack these exercises easily. These solutions give students knowledge about data handling. Solutions can be downloaded in PDF format on the Infinity Learn website.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>NCERT Exemplar Solutions Class 8 Maths Solutions Chapter 7 Algebraic Expression, Identities &amp; Factorization Subject specialists have designed NCERT Exemplar [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Class 8 Maths Solutions Chapter 7","_yoast_wpseo_title":"(Class 8 Maths Solutions Chapter 7) NCERT Exemplar Solutions","_yoast_wpseo_metadesc":"Free PDF download of NCERT Exemplar Solutions for Class 8 Maths Chapter 7 Algebraic Expression, Identities & Factorization.","custom_permalink":"study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/"},"categories":[153,161,105,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>(Class 8 Maths Solutions Chapter 7) NCERT Exemplar Solutions<\/title>\n<meta name=\"description\" content=\"Free PDF download of NCERT Exemplar Solutions for Class 8 Maths Chapter 7 Algebraic Expression, Identities &amp; Factorization.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"(Class 8 Maths Solutions Chapter 7) NCERT Exemplar Solutions\" \/>\n<meta property=\"og:description\" content=\"Free PDF download of NCERT Exemplar Solutions for Class 8 Maths Chapter 7 Algebraic Expression, Identities &amp; Factorization.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/\" \/>\n<meta property=\"og:site_name\" content=\"Infinity Learn by Sri Chaitanya\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/\" \/>\n<meta property=\"article:published_time\" content=\"2022-02-20T09:14:01+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-04-09T08:56:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1920\" \/>\n\t<meta property=\"og:image:height\" content=\"1008\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:site\" content=\"@InfinityLearn_\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasad Gupta\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"(Class 8 Maths Solutions Chapter 7) NCERT Exemplar Solutions","description":"Free PDF download of NCERT Exemplar Solutions for Class 8 Maths Chapter 7 Algebraic Expression, Identities & Factorization.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/","og_locale":"en_US","og_type":"article","og_title":"(Class 8 Maths Solutions Chapter 7) NCERT Exemplar Solutions","og_description":"Free PDF download of NCERT Exemplar Solutions for Class 8 Maths Chapter 7 Algebraic Expression, Identities & Factorization.","og_url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/","og_site_name":"Infinity Learn by Sri Chaitanya","article_publisher":"https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","article_published_time":"2022-02-20T09:14:01+00:00","article_modified_time":"2024-04-09T08:56:05+00:00","og_image":[{"width":1920,"height":1008,"url":"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2025\/04\/infinitylearn.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_creator":"@InfinityLearn_","twitter_site":"@InfinityLearn_","twitter_misc":{"Written by":"Prasad Gupta","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/infinitylearn.com\/surge\/#organization","name":"Infinity Learn","url":"https:\/\/infinitylearn.com\/surge\/","sameAs":["https:\/\/www.facebook.com\/InfinityLearn.SriChaitanya\/","https:\/\/www.instagram.com\/infinitylearn_by_srichaitanya\/","https:\/\/www.linkedin.com\/company\/infinity-learn-by-sri-chaitanya\/","https:\/\/www.youtube.com\/c\/InfinityLearnEdu","https:\/\/twitter.com\/InfinityLearn_"],"logo":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#logo","inLanguage":"en-US","url":"","contentUrl":"","caption":"Infinity Learn"},"image":{"@id":"https:\/\/infinitylearn.com\/surge\/#logo"}},{"@type":"WebSite","@id":"https:\/\/infinitylearn.com\/surge\/#website","url":"https:\/\/infinitylearn.com\/surge\/","name":"Infinity Learn by Sri Chaitanya","description":"Surge","publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/infinitylearn.com\/surge\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#webpage","url":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/","name":"(Class 8 Maths Solutions Chapter 7) NCERT Exemplar Solutions","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/#website"},"datePublished":"2022-02-20T09:14:01+00:00","dateModified":"2024-04-09T08:56:05+00:00","description":"Free PDF download of NCERT Exemplar Solutions for Class 8 Maths Chapter 7 Algebraic Expression, Identities & Factorization.","breadcrumb":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/infinitylearn.com\/surge\/"},{"@type":"ListItem","position":2,"name":"NCERT Exemplar Solutions Class 8 Maths Solutions Chapter 7 Algebraic Expression, Identities &#038; Factorisation"}]},{"@type":"Article","@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#article","isPartOf":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#webpage"},"author":{"@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05"},"headline":"NCERT Exemplar Solutions Class 8 Maths Solutions Chapter 7 Algebraic Expression, Identities &#038; Factorisation","datePublished":"2022-02-20T09:14:01+00:00","dateModified":"2024-04-09T08:56:05+00:00","mainEntityOfPage":{"@id":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-exemplar-solutions\/class-8\/maths\/chapter-7-algebraic-expressions-and-identities-factorisation\/#webpage"},"wordCount":1974,"publisher":{"@id":"https:\/\/infinitylearn.com\/surge\/#organization"},"articleSection":["Class 8","Maths","NCERT Exemplar Solutions","Study Materials"],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/infinitylearn.com\/surge\/#\/schema\/person\/143c89c9c2f5e56ed91f96dde47b0b05","name":"Prasad Gupta","image":{"@type":"ImageObject","@id":"https:\/\/infinitylearn.com\/surge\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/200104b443e586c76c46cadc113d931c?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/200104b443e586c76c46cadc113d931c?s=96&d=mm&r=g","caption":"Prasad Gupta"},"url":"https:\/\/infinitylearn.com\/surge\/author\/prasad\/"}]}},"_links":{"self":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/122776"}],"collection":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/comments?post=122776"}],"version-history":[{"count":0,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/posts\/122776\/revisions"}],"wp:attachment":[{"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/media?parent=122776"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/categories?post=122776"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/tags?post=122776"},{"taxonomy":"table_tags","embeddable":true,"href":"https:\/\/infinitylearn.com\/surge\/wp-json\/wp\/v2\/table_tags?post=122776"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}