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If $\omega$ is a complex cube root of unity, then $(x-y)(x \omega-y)\left(x \omega^2-y\right)=$
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The correct answer is:
$x^3-y^3$
$\begin{aligned} & (x-y)(x \omega-y)\left(x \omega^2-y\right) \\ & =\left(x^2 \omega-x y-x y \omega+y^2\right)\left(x \omega^2-y\right) \\ & =x^3-x^2 y\left(1+\omega+\omega^2\right)+x y^2\left(1+\omega+\omega^2\right)-y^3 \\ & =x^3-y^3 \quad\left(1+\omega+\omega^2=0\right)\end{aligned}$
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