Question

Factorise:

a⁶ – b⁶

Answer 1

We know that,

a³ + b³ = (a + b) (a² – ab + b²)    ...(1)

a³ – b³ = (a – b) (a² + ab + b²)    ...(2)

a⁶ – b⁶ = (a³)² – (b³)²

= (a³ + b³) (a³ – b³)

= (a + b) (a² – ab + b²) (a – b) (a² + ab + b²)

[From (1) and (2)]

= (a + b) (a – b) (a² – ab + b²) (a² + ab + b²)