Question

Factorise the following:

9a² – b² + 2bc – c²

Answer 1

Given, 9a² – b² + 2bc – c²

⇒ 9a² – (b² – 2bc + c²)

= 9a² – (b – c)²

⇒ (3a)² – (b – c)²

= [3a – (b – c)] [3a + (b – c)]

We know that,

(a + b)(a – b) = a² – b² 

Hence,

= [3a – (b – c)] [3a + (b – c)]