Question

Solve: $2{\sqrt{2a}}^3+3{\sqrt{3b}}^3+6{\sqrt{3a}}^{2}b+a{\sqrt{2ab}}^2$

Answer 1

Simplify: $2\sqrt{2}{a}^3+3\sqrt{3}{b}^3+6\sqrt{3}{a}^{2}b+9a\sqrt{2}ab$

$\Rightarrow (\sqrt{2}a{)}^3+(\sqrt{3}b{)}^3+3\left(\sqrt{2}a{)}^2\right(\sqrt{3}b)+3(\sqrt{2}a\left)\right(\sqrt{3}b{)}^2$

using identify $a^3+b^3+3a^{2}b+3a{b}^2=(a+b{)}^3$

$\Rightarrow (\sqrt{2}a+\sqrt{3}b{)}^3$