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By rohit.pandey1
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Updated on 24 Oct 2025, 13:03 IST
CBSE Class 8 Algebraic Expressions Worksheet — exam-oriented practice for Chapter 9: Algebraic Expressions and Identities with a clean answer key. This set covers terms, coefficients, like/unlike terms, addition–subtraction of expressions, multiplication, and NCERT-based identities—followed by mixed review questions for quick revision. Each page is structured for step-wise solving, making it ideal for daily homework, class tests, and periodic assessments.
Download the algebraic expressions and identities CBSE Class 8 Maths worksheet PDF for offline study and faster checking. If you’re searching for a focused practice worksheet that mirrors school-level difficulty and improves speed + accuracy, this resource is designed to help you master every concept—concept-wise drills first, then cumulative practice, and finally a consolidated Class 8 worksheet with answers to verify learning.
This free, downloadable Class 8 Maths Algebraic Expressions Worksheet PDF serves as a comprehensive Chapter 9 test paper for revision and practice. It covers all essential topics from the CBSE syllabus and includes detailed answers for self-evaluation.
Here’s what the worksheet includes:
Download the Algebraic Expressions and Identities Class 8 Worksheet PDF with Answers to test your understanding and strengthen your preparation for school exams. Regular practice using these worksheets ensures speed, accuracy, and confidence in algebraic operations.
Before you start solving the CBSE Class 8 Algebraic Expressions Worksheet, revise these important definitions and rules from Chapter 9: Algebraic Expressions and Identities. These basics will help you attempt every question confidently. If you need offline practice, use the Algebraic Expressions and Identities Class 8 Worksheet PDF linked on this page.
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An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
Examples: 5x + 7, 3y2 − 2x + 1
Each algebraic expression is made up of the following parts:
Understanding these parts is essential before attempting the algebraic expressions and identities Class 8 worksheet PDF.
Students often confuse like terms with unlike terms. Here is the difference:
Rule to Remember: Only like terms can be added or subtracted. For example, 7x + 2x = 9x, but 7x + 7y cannot be simplified further.
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This rule appears frequently in the Class 8 algebraic expressions worksheet with answers and in school tests.
In the CBSE Class 8 Algebraic Expressions and Identities chapter, expressions are classified by the number of terms:
TypeDefinitionExamples
| Monomial | Expression with only one term | 15, 7x, 4y2 |
| Binomial | Expression with two unlike terms | x + 5, 3a2 − 2b |
| Trinomial | Expression with three unlike terms | x2 + 5x + 6, a + b − c |
| Polynomial | Expression with one or more terms where exponents are non-negative integers | 2x3 + 3x2 − 5x + 1 |
These classifications are important for solving the CBSE Class 8 Algebraic Expressions Worksheet and other NCERT Solution-based practice questions.
After revising the concepts, practice with the Algebraic Expressions and Identities Class 8 Worksheet PDF. It includes exam-oriented questions and a complete answer key to help you check your solutions quickly.
This guide targets common “how-to” queries for Class 8 and builds confidence with fully solved examples. Use it alongside your algebraic expressions and identities Class 8 worksheet PDF for quick revision.
Strategy: Arrange expressions in standard form, combine like terms (same variables with the same powers), and keep signs carefully.
Question: Add the expressions: 3x + 4y − 7 and 5x − 2y + 9.
Final: The sum is 8x + 2y + 2. Use this approach in your addition of algebraic expressions Class 8 worksheet questions.
Subtract (2x − 3y + 5) from(7x + y − 4).
Remember: The word from reverses the natural order. This is a key step in the subtraction of algebraic expressions Class 8 worksheet problems.
Use the distributive property. Multiply coefficients, then apply exponent rules for the same base.
Question: Multiply 3x by (2x − 5).
Question: Multiply (2x + 3)(x − 5).
Use this pattern for any “how to multiply a binomial by a binomial Class 8” question in your multiplication of algebraic expressions Class 8 worksheet.
Strategy: When dividing a polynomial by a monomial, divide each term of the polynomial by the monomial.
Question: Simplify the expression: (6x2 − 9x + 12) ÷ 3x.
Answer: 2x − 3 + 4/x. Always reduce coefficients and subtract exponents for like bases when possible. This format is commonly asked as “simplify the expression” in the division of algebraic expressions Class 8 worksheet.
Mastering the standard algebraic identities Class 8 is the most important skill in CBSE Chapter 9: Algebraic Expressions and Identities. These identities help students simplify expressions, avoid calculation errors, and solve exam-style questions faster. Schools frequently test the ability to apply formulas in both numerical and algebraic forms, which is why this topic ranks among the most searched in Class 8 Maths worksheets. Use this page as a quick-reference guide and pair it with our Algebraic Expressions and Identities Class 8 Worksheet PDF for practice.
Here are the four standard algebraic identities for Class 8 students as prescribed in the CBSE Class 8 Maths syllabus. Learn and practice them well, as they form the foundation for all algebraic simplifications and factorizations in higher classes.
Let’s solve a few examples step by step to understand how to apply these identities effectively in your worksheet on algebraic identities Class 8.
Solution:
Hence, (102)² = 10404. You can similarly find (99)² by using (a − b)² identity.
Solution:
Therefore, (103)(104) = 10712. This is how to use the (x + a)(x + b) identity quickly without long multiplication.
Solution:
Final Answer: 9x² + 24xy + 16y²
This question is commonly asked in the Class 8 algebraic identities worksheet and helps in strengthening conceptual clarity.
Q1. Simplify the following expressions:
a) 3𝑥+5𝑥
b) 7𝑦−2𝑦+4
c) 6𝑎+3𝑏−2𝑎+𝑏
Q2. Expand the following expressions: a) 2(𝑥+4)2(x+4)
b) 3(𝑎−5)3(a−5)
c) 4(2𝑦+3)4(2y+3)
Q3. Combine like terms: a) 5𝑥+3𝑥−25
b) 8𝑎−3𝑎+6
c) 10𝑏+𝑏−7
Q4. Solve for x: a) 2𝑥+3=11
b) 5𝑥−2=18
c) 3𝑥+7=2𝑥+10
Q5. Perimeter of a Rectangle
A rectangle has a length of (3x+2) units and a width of (x−1) units. Write an expression for the perimeter of the rectangle.
Solution:
The formula for the perimeter (P) is P = 2(length + width).
P = 2((3x + 2) + (x - 1))
P = 2(4x + 1)
The perimeter of the rectangle is 8x + 2 units.
Q6. Books in a Book Shop
There are 6x + 8y shelves in a book shop and on each shelf there are 8x + 6y books. How many books are there in the book shop?
Solution:
Total books = (Number of shelves) × (Books per shelf).
Total books = (6x + 8y)(8x + 6y)
= 48x2 + 36xy + 64xy + 48y2
There are 48x2 + 100xy + 48y2 books.
Q7. Polynomial Subtraction
Subtract the sum of 11x2 + 5xy + 2y2 + 6 and 3x2 − 9xy − 4y2 + 5 from 8x2 − 13xy + 14y2.
Solution:
Step 1: Find the sum of the first two expressions.
Sum = (11x2 + 5xy + 2y2 + 6) + (3x2 − 9xy − 4y2 + 5) = 14x2 − 4xy − 2y2 + 11
Step 2: Subtract this sum from the third expression.
(8x2 − 13xy + 14y2) - (14x2 − 4xy − 2y2 + 11)
= 8x2 − 13xy + 14y2 - 14x2 + 4xy + 2y2 - 11
The result is -6x2 - 9xy + 16y2 - 11.
Q8. What Must Be Added?
What must be added to p2 − 8p + 11 to get 3p2 − 2p + 6?
Solution:
Subtract the initial expression from the final expression.
(3p2 − 2p + 6) - (p2 − 8p + 11)
= 3p2 − 2p + 6 - p2 + 8p - 11
You must add 2p2 + 6p - 5.
Q9. What Must Be Subtracted?
What must be subtracted from −p2 + 2q2 + 4r2 − 4pqr to get 2p2 − q2 − 3r2 + pqr?
Solution:
Subtract the final expression from the initial expression.
(−p2 + 2q2 + 4r2 − 4pqr) - (2p2 − q2 − 3r2 + pqr)
= -p2 + 2q2 + 4r2 − 4pqr - 2p2 + q2 + 3r2 - pqr
You must subtract -3p2 + 3q2 + 7r2 - 5pqr.
Q10. Multiplication by Distributive Law
Find the multiplication of (4m3 + 36m2n) × (-mn2⁄3) by using distributive law.
Solution:
(4m3 × -mn2/3) + (36m2n × -mn2/3)
= -4/3 m4n2 - 36/3 m3n3
The product is -4/3 m4n2 - 12m3n3.
Q11. Polynomial Division
Divide (p4 − 256) by (p + 4).
Solution:
Using polynomial long division, the quotient is p3 - 4p2 + 16p - 64 and the remainder is 0.
Q12. Quotient and Remainder
Find the quotient and remainder when (4r5 + 5r4 − 13r3 + 6r2 − 34r + 7) is divided by (r2 + 2r + 3).
Solution:
Using polynomial long division:
Quotient: 4r3 - 3r2 - 19r + 53
Remainder: -181r - 152
Q13. Amount Received by Each Person
If a sum of rupees (32a3 − 76a2 + 72a − 18) is divided equally among (8a − 3) persons. Find the amount received by each person.
Solution:
Divide the total sum by the number of persons using polynomial long division.
The amount received by each person is 4a2 - 8a + 6 rupees.
Q14. Perimeter of a Quadrilateral Field
If (3p + 5q), (9p + q), (p + 14q), and (5p − 6q) units are the lengths of the sides of a quadrilateral field, find the perimeter.
Solution:
The perimeter is the sum of the lengths of all sides.
(3p + 5q) + (9p + q) + (p + 14q) + (5p - 6q)
= (3+9+1+5)p + (5+1+14-6)q
The perimeter is 18p + 14q units.
Q15. Product of Two Numbers
The product of two numbers is (m6 − n6). If one of the numbers is (m − n), then find the other.
Solution:
Divide the product by the known number. You can use polynomial long division or factoring.
Factoring m6 - n6 gives (m-n)(m5 + m4n + m3n2 + m2n3 + mn4 + n5).
The other number is m5 + m4n + m3n2 + m2n3 + mn4 + n5.
Q16. Area Comparison
The length and breadth of a rectangular box are (x + 3y) and (5x − y) units respectively. Its perimeter is equal to the perimeter of a square box. Find how much the area of the rectangular box is less than that of the square.
Solution:
1. Perimeter of rectangle:2((x+3y)+(5x-y)) = 2(6x+2y) = 12x+4y
2. Side of square: The square's perimeter is also 12x+4y. So, its side is (12x+4y)/4 = 3x+y
3. Area of square:(3x+y)2 = 9x2+6xy+y2
4. Area of rectangle:(x+3y)(5x-y) = 5x2+14xy-3y2
5. Difference in area:(9x2+6xy+y2) - (5x2+14xy-3y2)
The rectangular box's area is 4x2 - 8xy + 4y2 units less than the square's.
| CBSE Class 8 Related Worksheets: | |
| Rational Numbers Worksheet | Factorisation Worksheet Class 8 Maths |
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An algebraic expression is a combination of variables, constants, and arithmetic operations (like addition, subtraction, multiplication). It does not have an equals sign (=). For example, 5x + 3y - 7 is an expression. An equation, on the other hand, always has an equals sign and states that two expressions are equal to each other. For example, 5x + 3y - 7 = 12 is an equation. Think of an expression as a phrase and an equation as a complete sentence.
'Like terms' are terms that have the exact same variables raised to the exact same powers. The coefficients (the numbers in front) can be different.
7x²y and -3x²y are like terms.7xy² and -3x²y are not like terms because the powers on x and y are different.You can only add or subtract like terms because you are combining quantities of the same thing. Think of it like fruit: you can add 3 apples and 4 apples to get 7 apples, but you cannot add 3 apples and 4 oranges to get "7 apple-oranges." Similarly, 3x² + 4x² becomes 7x², but 3x² + 4x cannot be simplified further.
The most common mistake is forgetting to change the sign of every term in the expression being subtracted. When you see a problem like Subtract (2a - 3b) from (5a + 4b), it means you are doing (5a + 4b) - (2a - 3b). The minus sign outside the bracket applies to both 2a and -3b.
5a + 4b - 2a - 3bAlways remember to distribute the negative sign to all the terms inside the parenthesis.
This is a crucial concept. The identity for (a+b)2 is a2+2ab+b2. It means you are multiplying the entire term (a+b) by itself. The term a2+b2 is missing the middle term, 2ab.
As you can see, the results are different. Never forget the middle 2ab term when squaring a binomial.