Worksheet on Factorisation

Worksheet of Factorisation for Grade 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