Answer
$38+12\sqrt{10}$
Work Step by Step
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ the given expression, $
(2\sqrt{5}+3\sqrt{2})^2
,$ is equivalent to
\begin{align*}
&
(2\sqrt{5})^2+2(2\sqrt{5})(3\sqrt{2})+(3\sqrt{2})^2
\\&=
4(5)+12\sqrt{10}+9(2)
\\&=
20+12\sqrt{10}+18
\\&=
(20+18)+12\sqrt{10}
\\&=
38+12\sqrt{10}
.\end{align*}
Hence, the product of the given expression is $
38+12\sqrt{10}
$.
