Question

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

Answer 1

$$\begin{gathered} 2\sqrt{2}{a}^3+16\sqrt{2}{b}^3+c^3-12abc={\left(\sqrt{2}a\right)}^3+{\left(2\sqrt{2}b\right)}^3+c^3-3\times \left(\sqrt{2}a\right)\times \left(2\sqrt{2}b\right)\times \left(c\right) \\ =\left(\sqrt{2}a+2\sqrt{2}b+c\right)\left[{\left(\sqrt{2}a\right)}^2+{\left(2\sqrt{2}b\right)}^2+c^2-\left(\sqrt{2}a\right)\times \left(2\sqrt{2}b\right)-\left(2\sqrt{2}b\right)\times \left(c\right)-\left(\sqrt{2}a\right)\times \left(c\right)\right] \\ =\left(\sqrt{2}a+2\sqrt{2}b+c\right)\left(2a^2+8b^2+c^2-4ab-2\sqrt{2}bc-\sqrt{2}ac\right) \end{gathered}$$