Question

Prove that (x-y)(xω-y)(xω 2 -y) = (x 3 -y 3 )

Answer 1

(x-y)(xω-y)(xω²-y)
=(x-y)(x²ω³-xyω²-xyω+y²)
=(x-y){x²-xy(ω+ω²)+y²}
[∵, ω³=1]
=(x-y)(x²-xy+y²)
[∵,  1+ω+ω²=0]
=x³-y³ (Proved)