Worksheet for Class 7 Maths for Chapter 5 Factorisation

The Factorisation Worksheet for Class 7 Maths is prepared to help students understand the concept of breaking down complex algebraic expressions into simpler factors. This worksheet includes a variety of questions based on H.C.F. method, common factors, grouping of terms, and special identities, that makes learning more interactive and effective.

By solving these problems, students can confidently handle algebraic equations. Each question is created in a step-by-step way to guide learners through the process of simplifying and factorising expressions correctly.

This Class 7 Maths Chapter 5 worksheet also includes answers and detailed solutions for self-assessment, making it an useful resource for exam preparation, daily practice, and concept revision. 

Class 7 Maths Worksheet Chapter 5 Factorisation

Instructions: Try each question. Write “Answer” to check your work.

Type 1: Fill in the Blanks

1. The common factor of 12x and 18x² is ________.

Answer: 6x

2. Factorisation means writing an expression as a ________ of its factors.

Answer: Product

3. a² - b² = ________.

Answer: (a + b)(a - b)

4. 5xy + 10x = 5x(______ + ______)

Answer: y + 2

Also Check: Simple Equations Class 7 Worksheet | Data Handling Class 7 Worksheet

5. The highest common factor is also called the ________ factor.

Answer: Greatest Common Factor (GCF)

Type 2: Multiple Choice Questions

6. Factorise x² + 7x + 10: 

a) (x + 5)(x + 2)

 b) (x + 10)(x + 1) 

c) (x - 5)(x - 2)

Answer: (x + 5)(x + 2)

7. Which of the following is a perfect square trinomial?
a) x² + 6x + 9 

b) x² - 5x + 8 

c) x² + 3x + 2

Answer: a) x² + 6x + 9

8. 4a² - 9b² is an example of:

a) Common factor type b) Difference of squares c) Perfect square

Answer: b) Difference of squares

Type 3: Factorise the Following

9. 15xy + 25x

Answer: 5x(3y + 5)

10. x² + 11x + 30

Answer: (x + 5)(x + 6)

11. 4m² - 49n²

Answer: (2m + 7n)(2m - 7n)

12. 6x²y - 9xy²

Answer: 3xy(2x - 3y)

Type 4: Factorise

13. Factorise completely: 2x³y - 18xy

Answer: 2xy(x² - 9) = 2xy(x + 3)(x - 3)

14. Simplify by factorisation: (3x² - 27) ÷ 6x

Answer: (x + 3)(x - 3) ÷ 2x

Also Check: NCERT Solutions for Class 7 Maths | Comparing Quantities Class 7 Worksheet 

Factorisation Questions for Class 7 with Answers

Q1. Find the H.C.F. of:

1. 8a²b³ and 12a³b²
2. 18x²y⁴z³, 24x³y²z⁴ and 30x⁴y³z²

Answer

(1) H.C.F. of 8a²b³ and 12a³b² = (H.C.F. of 8, 12) × (a², a³) × (b³, b²) = 4a²b²
(2) H.C.F. of 18x²y⁴z³, 24x³y²z⁴, 30x⁴y³z² = (H.C.F. of 18, 24, 30) × (lowest powers) = 6x²y²z²

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Q2. Find the H.C.F. of:

1. 10m³n² and 25m²n³
2. 28x²y³z⁴, 42x³y²z⁵ and 56x⁴y⁴z³

Answer

(1) H.C.F. = (H.C.F. of 10, 25) × (m³, m²) × (n², n³) = 5m²n²
(2) H.C.F. = (H.C.F. of 28, 42, 56) × (lowest powers of x, y, z) = 14x²y²z³

Q3. Factorise:

1. 7x²y + 14xy²
2. 8a³b - 12a²b²
3. 9p²q - 15pq² + 6pq
4. 20x²y³ - 10x³y²

Answer

(1) 7x²y + 14xy² = 7xy(x + 2y)
(2) 8a³b - 12a²b² = 4a²b(2a - 3b)
(3) 9p²q - 15pq² + 6pq = 3pq(3p - 5q + 2)
(4) 20x²y³ - 10x³y² = 10x²y²(2y - x)

Q4. Factorise the following using common binomial terms:

1. 5x(a + 2b) + 10y(a + 2b)
2. 9m(p - q) - 12n(p - q)
3. 7a²(b + 1) - 14a(b + 1)
4. x(x + 3y) - 4y(x + 3y)

Answer

(1) = 5(x + 2y)(a + 2b)
(2) = 3(3m - 4n)(p - q)
(3) = 7a(a - 2)(b + 1)
(4) = (x - 4y)(x + 3y)

Q5. Simplify and Factorise Completely:

1. 2a²b - 6ab² + 8ab
2. 12x²y² - 18xy³ + 6x³y
3. 5p(p - 3) - 2q(p - 3)
4. 9x(x - y) - 4y(x - y)

Answer

(1) = 2ab(a - 3b + 4)
(2) = 6xy²(2x - 3y + x²/y)
(3) = (5p - 2q)(p - 3)
(4) = (9x - 4y)(x - y)