Question

Verify the following:

(a + b + c)(a² + b² + c² – ab – bc – ca) = a³ + b³ + c³ – 3abc

Answer 1

Taking L.H.S. = (a + b + c)(a² + b² + c² – ab – bc – ca)

= a(a² + b² + c² – ab – bc – ca) + b(a² + b² + c² – ab – bc – ca) + c(a² + b² + c² – ab – bc – ca)  ...[Distributive law]

= a³ + ab² + ac² – a²b – abc – a²c + ba² + b³ + bc² – b²a – b²c – bca + ca² + cb² + c³ – cab – c²b – c²a

= a³ + b³ + c³ – 3abc

= R.H.S.

Hence verified.