Question

Factorise:
$a^3-2\sqrt{2}{b}^3$

Answer 1

We know the identity $a^3-b^3=(a-b)(a^2+b^2+ab)$

Using the above identity, the equation $1-x^3$ can be factorised as follows:

$a^3-2\sqrt{2}{b}^3=(a{)}^3-{\left(\sqrt{2}b\right)}^3=(a-\sqrt{2}b)\left[\right(a{)}^2+{\left(\sqrt{2}b\right)}^2+(a\times \sqrt{2}b)]=(a-\sqrt{2}b)(a^2+2b^2+\sqrt{2}ab)$

Hence, $a^3-2\sqrt{2}{b}^3=(a-\sqrt{2}b)(a^2+2b^2+\sqrt{2}ab)$