How do you factor completely $a^3-10$ ?

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Answer 1 · 2017-07-13T07:09:35

$a^3 -10 = (a-root3 10)(a^2+aroot3 10 +root3 10^2)$

$10$ is not a perfect cube, but we can show its cube root as $root3 10$ which is an irrational number.

The difference of cubes factorises as:
$x^3 -y^3 = (x-y)(x^2 +xy+y^2)$

$a^3 -10 = (a-root3 10)(a^2+aroot3 10 +root3 10^2)$

How do you factor completely a^3-10a^3-10?