Question

Factorise the following expressions.

(i) 49y² + 84yz + 36z²

(ii) 4x² − 8x + 4

(iii) 121b² − 88bc + 16c²

Answer 1

(i) 49y² + 84yz + 36z² 

= (7y)² + 2 × (7y) × (6z) + (6z)²

= (7y + 6z)²    [(a + b)² = a² + 2ab + b²]

(ii) 4x² − 8x + 4 

= (2x)² − 2 (2x) (2) + (2)²

= (2x − 2)²    [(a − b)² = a² − 2ab + b²]

= [(2) (x − 1)]² = 4(x − 1)²

(iii) 121b² − 88bc + 16c² 

= (11b)² − 2 (11b) (4c) + (4c)²

= (11b − 4c)²    [(a − b)² = a² − 2ab + b²]