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CBSE Worksheet on Algebraic Expressions For Class 8
By rohit.pandey1
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Updated on 22 Sep 2025, 17:09 IST
Download and read a free PDF of the CBSE Class 8 Algebraic Expressions worksheet. Students and teachers of Class 8 Mathematics can access free printable worksheets in PDF format. These Class 8 Math worksheets are prepared according to the latest syllabus and exam pattern. Class 8 students should practice the questions and answers provided here to enhance their knowledge and skills.
Download Free Algebraic Expressions Worksheet (PDF Download)
This worksheet provides practice questions to help you master algebraic expressions. It contains over 25 carefully selected problems. The questions are divided into five sections. Each section is designed to build your skills step-by-step. Click the button below to download your free PDF, which includes a full answer key.
Worksheet 1 – Algebraic Expressions For Class 8
Section 1: Types of Algebraic Expressions
1. Identify the type of algebraic expressions: - 4x + 5 - 7y² - 3a + 2b + 4
2. Classify the following as monomial, binomial, or polynomial: - 6m - 2x² + 3x - 5x³ + 4x² + 3x + 2
Section 2: Simplification of Algebraic Expressions
1. Simplify the following expressions: - 2x + 3x - 4a - 2a + 5 2.
Combine like terms in the following: - 7m + 3n + 5m - 2n
Section 3: Basic Operations on Algebraic Expressions
1. Add the following expressions: - (3x + 4) + (5x + 6)
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2. Subtract the following expressions: - (7a + 5) - (2a + 3)
3. Multiply the following expressions: - 3y × 4y
4. Divide the following expressions: - 8x² ÷ 2x
Section 4: Solving Linear Equations
1. Solve for x: - 3x + 5 = 20
2. Solve for y: - 2y - 4 = 10
Section 5: Expand and simplify the following: - (x + 3)(x + 2)
2. Factorize the following expressions: - x² + 5x + 6
Also Read: Worksheets for Class 8 Rational Number
Worksheet 2 – Algebraic Expressions For Class 8
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.
Also Read: Algebraic Expressions Formulas
Algebraic Expressions Worksheet For Class 8 PDF
Understanding algebraic expressions is crucial for solving various mathematical problems and equations. Mastering these concepts helps students to excel in Class 8 Mathematics. Infinity Learn provides Algebraic Expressions Worksheets for Class 8 in PDF format to facilitate easy self-practice.
Click on these links to download Algebraic Expressions Worksheet For Class 8 PDF:
Algebraic Expressions Worksheet 1 For Class 8 PDF
Algebraic Expressions Worksheet 2 For Class 8 PDF
Worksheet on Algebraic Expressions for Class 8 Maths CBSE
The worksheets and assignments for Class 8 Maths, including the Worksheet on Algebraic Expressions, are readily available on Infinity Learn platform. Students can easily download, print, or view these resources in PDF format, accommodating different learning styles and technological access. Whether using a computer, tablet, or smartphone, students can engage with these materials to strengthen their understanding of algebraic expressions. After completing the worksheets, students can further practice with additional resources like online quizzes and exercises to reinforce their knowledge. Regular practice is crucial for building a solid foundation and mastering algebraic concepts in the CBSE curriculum.
In mastering algebraic expressions is a crucial part of the Class 8 Maths curriculum under CBSE. The worksheets and assignments provided help students build a strong foundation in algebra, which is essential for advanced mathematical studies. Utilizing online resources allows for flexible and accessible learning, enabling students to practice and reinforce their skills effectively. Regular practice through these materials not only enhances problem-solving abilities but also boosts confidence in handling complex algebraic concepts. By consistently engaging with these resources, students can achieve a thorough understanding and excel in their maths exam.
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FAQs for a Worksheet on Algebraic Expressions
What is the difference between an 'expression' and an 'equation'?
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.
What are 'like terms' and why can I only add or subtract them?
'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.
- Examples:
7x²yand-3x²yare like terms. - Non-Examples:
7xy²and-3x²yare 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.
What is the most common mistake when subtracting algebraic expressions?
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.
- Incorrect:
5a + 4b - 2a - 3b - Correct: 5a + 4b - 2a + 3b = 3a + 7b
Always remember to distribute the negative sign to all the terms inside the parenthesis.
What is the difference between (a+b)2 and a2+b2?
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.
- Example: Let a=3 and b=4.
- (3+4)2=7^2=49.
- 3^2+4^2=9+16=25.
As you can see, the results are different. Never forget the middle 2ab term when squaring a binomial.