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If $x = a + b, y = a ω + b ω^{2}$ and $z = a ω^{2} + b ω$ the value of $x^{3} + y^{3} + z^{3}$ is equal to

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$a^{3} + b^{3}$

$3 (a^{3} + b^{3})$

$(a^{2} - a b + b^{2})$

answer is C.

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Detailed Solution

$\begin{array}{l} x + y + z = a + b + a ω + b ω^{2} + a ω^{2} + b ω = 0 \\ \Rightarrow x^{3} + y^{3} + z^{3} = 3 x y z \\ = 3 (a + b) (a ω + b ω^{2}) (a ω^{2} + b ω) \\ = 3 (a^{3} + b^{3}) . \end{array}$

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