Question

Simplify the following expression:

$\left(iii\right)(2\sqrt{5}+3\sqrt{2}{)}^2$

Answer 1

Given: $(2\sqrt{5}+3\sqrt{2}{)}^2$
Using identity, $(a+b{)}^2=a^2+2ab+b^2$
$(2\sqrt{5}+3\sqrt{2}{)}^2$
$=(2\sqrt{5}{)}^2+2\times (2\sqrt{5})\times (3\sqrt{2})+(3\sqrt{2}{)}^2$
$=20+12\sqrt{10}+18$
$=38+12\sqrt{10}$