Question

Simplify:

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

Answer 1

We have,

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

= a³ + ab² + a²b – ba² – b³ – ab² – a³ – ab² + a²b – ba² – b³ + ab²

= (a³ – a³) + (– b³ – b³) + (ab² – ab²) + (a²b – a²b + a²b – a²b)

= 0 – 2b³ + 0 + 0 + 0

= – 2b³