Question

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

Answer 1

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

$\therefore 2a^2+2\sqrt{6}ab+3b^2$
$=(\sqrt{2a}{)}^2+2\times \sqrt{2a\times }\sqrt{3b}+(\sqrt{3b}{)}^2$
$=(\sqrt{2a}+\sqrt{3b}{)}^2[\because x^2+y^2+2xy=(x+y{)}^2]$

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