Worksheet on Factorisation for Class 8

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: