Factorize:
$a^{3} - 0 - 216$

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Solution

We have,
$a^{3} - 0 - 216$
$\Rightarrow (a^{3} - 216)$
$\Rightarrow (a^{3} - 6^{3})$

Since,
$x^{3} - y^{3} = (x - y) (x^{2} + y^{2} + x y)$

Therefore,
$\Rightarrow (a^{3} - 6^{3}) = (a - 6) (a^{2} + 6^{2} + a 6)$

$\Rightarrow (a^{3} - 6^{3}) = (a - 6) (a^{2} + 36 + 6 a)$

Hence, this is the answer.

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