Question

Factorize :
$2\sqrt{2}{a}^3+16\sqrt{2}{b}^3+c^3-12abc$.

Answer 1

$2\sqrt{2}{a}^3+16\sqrt{2}{b}^3+c^3-12abc$

$=(\sqrt{2a}{)}^3+(\sqrt{8b}{)}^3+(c{)}^3-3(\sqrt{2}\left)\right(\sqrt{8}\left)\right(abc)$

$=(\sqrt{2a}{)}^3+\sqrt{8b}+c)(2a^2+8b^2+c^2-4ab-\sqrt{2a}-\sqrt{8}bc)$

$=(\sqrt{2a}+2\sqrt{2b}+c)(2a^2+8b^2+c^2-4ab-\sqrt{2ac}-2\sqrt{2}bc)$