Factorise.
$x^{3} + 64 y^{3}$

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Solution

It is known that,

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$

According to the given condition

$x^{3} + 64 y^{3} = x^{3} + {(4 y)}^{3}$

$\Rightarrow x^{3} + {(4 y)}^{3} = (x + 4 y) (x^{2} + 16 y^{2} - 4 x y)$

Hence, the answer is $(x + 4 y) (x^{2} + 16 y^{2} - 4 x y) .$

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