Question

Factorise the following:

a² – 9b² + 6b – 1

Answer 1

Given a² – 9b² + 6b – 1

⇒ a² – [(3b)² – 2 × 3b × 1 + 1²] 

⇒ a² – (3b – 1)²

We know that,

⇒ (a + b) (a – b) = a² – b²

Hence,

⇒ (a + 3b – 1) (a – 3b + 1)