Factorize $27 x^{3} - 64 y^{3}$

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Solution

$27 x^{3} - 64 y^{3} = (3 x)^{3} - (4 y)^{3}$
$= (3 x - 4 y) [(3 x)^{2} + (3 x) (4 y) + (4 y)^{2}]$
$= (3 x + 4 y) (9 x^{2} + 12 x y + 16 y^{2})$

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