Question

if a+b+c =0 show that a cube + b cube + c cube =3 ABC

Answer 1

acube+bcube+ccube-3abc=(a+b+c)(asquare+bsquare+csquare-ab-bc-ca)

But a+b+c=0 so, RHS=0,acube+bcube+ccube=3abc

Answer 2

This way it is proved