Question

Factorize the given polynomial expression

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

Answer 1

Given that, $2a^2+2\sqrt{6}ab+3b^2$

$=(\sqrt{2}a{)}^2+2(\sqrt{3}\left)\right(\sqrt{2})ab+(\sqrt{3}b{)}^2$ $[\because A^2+2AB+B^2=(A+B{)}^2]$

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

$\therefore 2a^2+2\sqrt{6}ab+3b^2=(\sqrt{2}a+\sqrt{3}b{)}^2$