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(A) Given the expression: $(a + b)(a + b\omega)(a + b\omega^2)$ Since $\omega$ is a non-real cube root of unity,we know that $1 + \omega + \omega^2 =

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$a^3 + b^3$

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(A) Given the expression: $(a + b)(a + b\omega)(a + b\omega^2)$ Since $\omega$ is a non-real cube root of unity,we know that $1 + \omega + \omega^2 = 0$ and $\omega^3 = 1$. First,multiply the last two terms: $(a + b\omega)(a + b\omega^2) = a^2 + ab\omega^2 + ab\omega + b^2\omega^3 = a^2 + ab(\omega + \omega^2) + b^2(1)$. Since $\omega + \omega^2 = -1$,this simplifies to: $a^2 - ab + b^2$. Now,multiply by the first term: $(a + b)(a^2 - ab + b^2) = a^3 + b^3$.

If $\omega$ is a non-real cube root of unity,then $(a + b)(a + b\omega)(a + b\omega^2)$ is equal to:

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