If omega is a complex cube root of unity,then | vedclass

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(C) Given the expression: $(x - y)(x\omega - y)(x\omega^2 - y)$First,multiply the first two terms:$(x - y)(x\omega - y) = x^2\omega - xy - xy\omega +

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$x^3 - y^3$

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(C) Given the expression: $(x - y)(x\omega - y)(x\omega^2 - y)$First,multiply the first two terms:$(x - y)(x\omega - y) = x^2\omega - xy - xy\omega + y^2$Now,multiply the result by the third term $(x\omega^2 - y)$:$= (x^2\omega - xy - xy\omega + y^2)(x\omega^2 - y)$$= x^3\omega^3 - x^2y\omega - x^2y\omega^2 + xy^2 - x^2y\omega^3 + xy^2\omega + xy^2\omega^2 - y^3$$= x^3(1) - x^2y(\omega + \omega^2 + 1) + xy^2(1 + \omega + \omega^2) - y^3$Since $1 + \omega + \omega^2 = 0$:$= x^3 - x^2y(0) + xy^2(0) - y^3$$= x^3 - y^3$

If $\omega$ is a complex cube root of unity,then $(x - y)(x\omega - y)(x\omega^2 - y) = $

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