{"id":665493,"date":"2023-07-25T15:10:29","date_gmt":"2023-07-25T09:40:29","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=665493"},"modified":"2025-05-16T14:46:07","modified_gmt":"2025-05-16T09:16:07","slug":"a-b-whole-cube-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/","title":{"rendered":"a+b Whole Cube Formula"},"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\/topics\/a-b-whole-cube-formula\/#ab_Whole_Cube_Formula\" title=\"a+b Whole Cube Formula\">a+b Whole Cube Formula<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/#ab_Whole_Cube_Formula_DerivationProof\" title=\"a+b Whole Cube Formula Derivation\/Proof\">a+b Whole Cube Formula Derivation\/Proof<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/#ab_Whole_Cube_Formula_with_Examples\" title=\"a+b Whole Cube Formula with Examples\">a+b Whole Cube Formula with Examples<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/#FAQs_on_ab_Whole_Cube_Formula\" title=\"FAQs on a+b Whole Cube Formula\">FAQs on a+b Whole Cube Formula<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/#What_is_the_formula_for_a_b_whole_cube\" title=\"What is the formula for (a + b) whole cube?\">What is the formula for (a + b) whole cube?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/#What_is_the_formula_for_a_-_b_whole_cube\" title=\"What is the formula for (a &#8211; b) whole cube?\">What is the formula for (a &#8211; b) whole cube?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/#What_is_the_formula_for_a_b_whole_square\" title=\"What is the formula for (a + b) whole square?\">What is the formula for (a + b) whole square?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/#What_is_the_identity_of_a_b%C2%B3\" title=\"What is the identity of (a + b)\u00b3?\">What is the identity of (a + b)\u00b3?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/a-b-whole-cube-formula\/#What_is_the_formula_for_a%C2%B3_b%C2%B3\" title=\"What is the formula for a\u00b3 + b\u00b3?\">What is the formula for a\u00b3 + b\u00b3?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p style=\"text-align: justify;\">The algebraic formula of a+b Whole Cube is a fundamental and powerful mathematical expression widely used in various competitive exams and academic settings. The a+b Whole Cube Formula allows us to efficiently expand the cube of a binomial expression (a+b) and simplifies calculations involving polynomial expressions. Understanding the a+b Whole Cube Formula is crucial for students, particularly those in class 10th, as it enables them to expedite mathematical computations and solve problems with ease.<\/p>\n<p style=\"text-align: justify;\">In this discussion, we will delve into the derivation of the a + b Whole Cube formula, explore its applications, and provide illustrative examples to demonstrate its practical utility. Mastering the a+b Whole Cube formula will enhance problem-solving skills and lay a strong foundation for tackling more advanced mathematical concepts in the future.<\/p>\n<h2 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"ab_Whole_Cube_Formula\"><\/span>a+b Whole Cube Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\">In algebra, the cube of the sum of two algebraic terms, a and b, is represented as (a + b)\u00b3. This powerful formula is essential in expanding and simplifying polynomial expressions. To compute (a + b)\u00b3, we break it down into three components: the cube of &#8216;a,&#8217; the cube of &#8216;b,&#8217; and the product of 3ab multiplied by the sum of &#8216;a&#8217; and &#8216;b.&#8217;<br \/>\nThe expression can be written as:<\/p>\n<p style=\"text-align: justify;\">(a + b)<sup>3<\/sup> = a\u00b3 + b\u00b3 + 3ab(a + b)<br \/>\n(a + b)<sup>3<\/sup> = a\u00b3 + b\u00b3 + 3a\u00b2b + 3ab\u00b2<\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"ab_Whole_Cube_Formula_DerivationProof\"><\/span>a+b Whole Cube Formula Derivation\/Proof<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">To derive the formula for (a + b)\u00b3, we start with the multiplication of three algebraic expressions of the binomial (a + b)(a + b)(a + b) = (a + b)\u00b3. Then, we simplify the expression step by step as follows:<\/p>\n<p style=\"text-align: justify;\"><strong>Step 1:<\/strong> Multiply the first two binomials using the distributive property.<\/p>\n<p style=\"text-align: justify;\">(a + b)(a + b) = a\u00b2 + 2ab + b\u00b2<\/p>\n<p style=\"text-align: justify;\"><strong>Step 2:<\/strong> Now, multiply the result of step 1 with the third binomial (a + b).<\/p>\n<p style=\"text-align: justify;\">(a\u00b2 + 2ab + b\u00b2)(a + b) = a\u00b3 + a\u00b2b + 2a\u00b2b + 2ab\u00b2 + ab\u00b2 + b\u00b3<\/p>\n<p style=\"text-align: justify;\"><strong>Step 3:<\/strong> Combine like terms in the expression obtained in step 2.<\/p>\n<p style=\"text-align: justify;\">a\u00b3 + (a\u00b2b + 2a\u00b2b) + (2ab\u00b2 + ab\u00b2) + b\u00b3 = a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3<\/p>\n<p style=\"text-align: justify;\"><strong>Step 4:<\/strong> Notice that the terms (a\u00b2b + 2a\u00b2b) and (2ab\u00b2 + ab\u00b2) can be simplified to 3a\u00b2b and 3ab\u00b2, respectively.<\/p>\n<p style=\"text-align: justify;\"><strong>Step 5:<\/strong> Factor out 3ab from the last three terms.<br \/>\na\u00b3 + 3ab(a + b) + b\u00b3<\/p>\n<p style=\"text-align: justify;\">Thus, the final result is the formula for (a + b)\u00b3:<\/p>\n<p style=\"text-align: justify;\">(a + b)<sup>3<\/sup> = a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3<\/p>\n<p style=\"text-align: justify;\">This a+b Whole Cube formula is essential in expanding the cube of a binomial and simplifying expressions in algebraic equations, making mathematical calculations more efficient and straightforward.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/infinitylearn.com\/surge\/formulas\/math-formulas\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Math Formulas<\/button><\/a> <a href=\"https:\/\/infinitylearn.com\/surge\/topics\/pythagorean-triples\/\"><button class=\"btn btn-dark mx-2 my-2 px-4\" style=\"border-radius: 50px;\" type=\"button\">Pythagorean Triple<\/button><\/a><\/p>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"ab_Whole_Cube_Formula_with_Examples\"><\/span>a+b Whole Cube Formula with Examples<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\">The examples below demonstrate the application of the a+b Whole Cube Formula to calculate the cube of various binomial expressions. By understanding and memorizing the a+b Whole Cube formula, one can quickly and efficiently solve such algebraic problems, making mathematical computations faster and more convenient.<\/p>\n<p style=\"text-align: justify;\"><strong>Example 1: Find the cube of (2x + 3y).<\/strong><\/p>\n<p style=\"text-align: justify;\">Solution:<br \/>\nUsing the (a + b) Whole Cube formula:<br \/>\n(2x + 3y)\u00b3 = (2x)\u00b3 + 3(2x)\u00b2(3y) + 3(2x)(3y)\u00b2 + (3y)\u00b3<br \/>\n= 8x\u00b3 + 36x\u00b2y + 54xy\u00b2 + 27y\u00b3<\/p>\n<p style=\"text-align: justify;\"><strong>Example 2: Calculate the cube of (a &#8211; 5b).<\/strong><\/p>\n<p style=\"text-align: justify;\">Solution:<br \/>\nUsing the (a + b) Whole Cube formula:<br \/>\n(a &#8211; 5b)\u00b3 = (a)\u00b3 + 3(a)\u00b2(-5b) + 3(a)(-5b)\u00b2 + (-5b)\u00b3<br \/>\n= a\u00b3 &#8211; 15a\u00b2b + 75ab\u00b2 &#8211; 125b\u00b3<\/p>\n<p style=\"text-align: justify;\"><strong>Example 3: Determine the cube of (3x\u00b2 &#8211; 4y).<\/strong><\/p>\n<p style=\"text-align: justify;\">Solution:<br \/>\nUsing the (a + b) Whole Cube formula:<br \/>\n(3x\u00b2 &#8211; 4y)\u00b3 = (3x\u00b2)\u00b3 + 3(3x\u00b2)\u00b2(-4y) + 3(3x\u00b2)(-4y)\u00b2 + (-4y)\u00b3<br \/>\n= 27x^6 &#8211; 108x^4y + 144x\u00b2y\u00b2 &#8211; 64y\u00b3<\/p>\n<h2 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"FAQs_on_ab_Whole_Cube_Formula\"><\/span>FAQs on a+b Whole Cube Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\">\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_formula_for_a_b_whole_cube\"><\/span>What is the formula for (a + b) whole cube?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe formula for (a + b) whole cube is (a + b)\u00b3 = a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3. \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<h3>What is the formula for (a - b) whole cube?<\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe formula for (a - b) whole cube is (a - b)\u00b3 = a\u00b3 - 3a\u00b2b + 3ab\u00b2 - b\u00b3. \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<h3><span class=\"ez-toc-section\" id=\"What_is_the_formula_for_a_b_whole_square\"><\/span>What is the formula for (a + b) whole square?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe formula for (a + b) whole square is (a + b)\u00b2 = a\u00b2 + 2ab + b\u00b2. \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<h3><span class=\"ez-toc-section\" id=\"What_is_the_identity_of_a_b%C2%B3\"><\/span>What is the identity of (a + b)\u00b3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe identity of (a + b)\u00b3 is a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3. \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<h3><span class=\"ez-toc-section\" id=\"What_is_the_formula_for_a%C2%B3_b%C2%B3\"><\/span>What is the formula for a\u00b3 + b\u00b3?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe formula for a\u00b3 + b\u00b3 is (a + b)(a\u00b2 - ab + b\u00b2). \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 is the formula for (a + b) whole cube?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula for (a + b) whole cube is (a + b)\u00b3 = a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3.\"\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\": \"What is the formula for (a - b) whole cube?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula for (a - b) whole cube is (a - b)\u00b3 = a\u00b3 - 3a\u00b2b + 3ab\u00b2 - b\u00b3.\"\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\": \"What is the formula for (a + b) whole square?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula for (a + b) whole square is (a + b)\u00b2 = a\u00b2 + 2ab + b\u00b2.\"\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\": \"What is the identity of (a + b)\u00b3?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The identity of (a + b)\u00b3 is a\u00b3 + 3a\u00b2b + 3ab\u00b2 + b\u00b3.\"\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\": \"What is the formula for a\u00b3 + b\u00b3?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The formula for a\u00b3 + b\u00b3 is (a + b)(a\u00b2 - ab + b\u00b2).\"\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>The algebraic formula of a+b Whole Cube is a fundamental and powerful mathematical expression widely used in various competitive exams [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"a+b Whole Cube Formula","_yoast_wpseo_title":"a+b Whole Cube Formula - (a +b )^3 Formula and Derivation","_yoast_wpseo_metadesc":"The formula (a + b)^3 is used to expand the cube of a binomial. Its derivation involves applying the distributive property three times.","custom_permalink":"topics\/a-b-whole-cube-formula\/"},"categories":[8594,8591],"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>a+b Whole Cube Formula - (a +b )^3 Formula and Derivation<\/title>\n<meta name=\"description\" content=\"The formula (a + b)^3 is used to expand the cube of a binomial. 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Its derivation involves applying the distributive property three times.","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\/topics\/a-b-whole-cube-formula\/","og_locale":"en_US","og_type":"article","og_title":"a+b Whole Cube Formula - (a +b )^3 Formula and Derivation","og_description":"The formula (a + b)^3 is used to expand the cube of a binomial. 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