Using cube root of unity factorize:
$a^{2} - a b + b^{2}$ .

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Solution

Now,
$a^{2} - a b + b^{2}$

$= a^{2} + (ω + ω^{2}) a b + b^{2} ω^{3}$ [ Since $1 + ω + ω^{2} = 0$ and $ω^{3} = 1$ ]

$a^{2} - a b + b^{2} = (a + b ω) (a + b ω^{2})$ .

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