Worksheet on Factorisation for Class 8

Breaking numbers into smaller parts reveals hidden patterns with our printable grade 8 factorisation practice questions that teach decomposition techniques. Students learn to find common factors and factor algebraic expressions. Each exercise develops analytical thinking while building mathematical skills. Learners discover elegant solutions through systematic factoring methods. Download free class 8 factorisation worksheet PDF for mathematical insight.

Solved Questions on Factorisation

1. Factorise the following: 121y²z² − 66xyz + 9x² − 9x + 33yz

a) (3x − 11yz)(11yz − 3x + 3)
b) (3x − 11yz)(11yz + 3x − 3)
c) (11yz − 3x)(11yz − 3x + 3)
d) (11yz − 3x)(11yz + 3x − 3)

Answer: c) (11yz − 3x)(11yz − 3x + 3)  

Explanation: 121y²z² − 66xyz + 9x² − 9x + 33yz
= [121y²z² − 66xyz + 9x²] + [33yz − 9x]
= [(11yz)² − 2(11yz)(3x) + (3x)²] + [3(11yz − 3x)] [Using a² − 2ab + b² = (a − b)²]
= [(11yz − 3x)²] + [3(11yz − 3x)]
= [(11yz − 3x)(11yz − 3x)] + [3(11yz − 3x)] [Using (a − b)² = (a − b)(a − b)]
= (11yz − 3x)[(11yz − 3x) + 3]
= (11yz − 3x)(11yz − 3x + 3)

2. Evaluate (using factors): 401² × 399 − 399³

a) 632400
b) 634400
c) 636400
d) 638400

Answer: d) 638400

Explanation: 401² × 399 − 399³  
= 401² × 399 − 399 × 399² 
= 399 × (401² − 399²)
= 399 × (401 + 399)(401 − 399) [By using: a² − b² = (a + b)(a − b)]
= (400  − 1) × (800)(2) [399 can be written as (400 − 1)]
= (400  − 1) × 1600
= 1600 × 400  − 1600 × 1
= 640000 − 1600
= 638400

3. Which of the following option is equal to (x + $\frac{\frac{3}{}}{\frac{x}{}}$)² − (x − $\frac{\frac{3}{}}{\frac{x}{}}$)² ?

a) 0
b) 6
c) 9
d) 12

Answer: d) 12

Explanation:

4. Simplify the following expression:

a) 1520
b) 1620
c) 1720
d) 1820

Answer: b) 1620

Explanation:

5. What is the quotient of the following expression?

(p⁴ – 81)(p² + 4p – 12) ÷ (p³ + 27 + 3p² + 9p) 

a) (p – 2)(p – 3) (p + 6)
b) (p + 2)(p + 3)(p – 6)
c) (p – 2)(p + 3)(p – 6)
d) (p – 2)(p + 3)(p + 6)

Answer: a) (p – 2)(p – 3) (p + 6)

Explanation: