Question

Verify the following:

(a – b)(a – b)(a – b) = a³ – 3a²b + 3ab² – b³ 

Answer 1

Taking L.H.S. = (a – b)(a – b)(a – b)

= (a – b)(a – b)²

= (a – b)(a² – 2ab + b²)  ...[Using the identity, (a – b)² = a² – 2ab + b²]

= a(a² – 2ab + b²) – b(a² – 2ab + b²)

= a³ – 2a²b + ab² – ba² + 2ab² – b³

= a³ – 3a²b + 3ab² – b³  ...[Adding like terms]

= R.H.S.

Hence verified.