Prove that- x3-y3-x-yx-y-x-y-2- - being cube root of unity-

Now, x^3 y^3 =(x y)(x^2+xy+y^2) =(x y){x^2 (ω+ω^2)xy+y^2ω^3} #160; #160; [ Since ω^3=1 and 1+ω+ω^2=0 ] =(x y)(x yω)(x yω^2) . ...

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Algebraic Identities

Prove that: ...

Question

Prove that:
$x^{3} - y^{3} = (x - y) (x - y ω) (x - y ω^{2})$ . $ω$ being cube root of unity.

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