Question

Factorise:

a² – 4b² + a³ – 8b³ – (a – 2b)²

Answer 1

Given, a² – 4b² + a³ – 8b³ – (a – 2b)²

{(a)² – (2b)²} + {(a)³ – (2b)³} – (a – 2b)²

⇒ (a + 2b) (a – 2b) + {(a – 2b) (a² + 2ab + 4b²)} – (a – 2b)²

Taking (a – 2b) as common from all the terms, we get,

(a – 2b) {(a + 2b) + (a² + 2ab + 4b²) – (a – 2b)}

⇒ (a – 2b) (a + 2b + a² + 2ab + 4b² – a + 2b)

⇒ (a – 2b) (`\cancel(a)` + 2b + a² + 2ab + 4b² – `\cancel(a)` + 2b)

⇒ (a – 2b) (a² + 2ab + 4b + 4b²)

Hence, the required is (a – 2b) (a² + 2ab + 4b + 4b²).