Simplify the following expressions:$ (2 \sqrt{5}+3 \sqrt{2})^{2} $

Given:

\( (2\sqrt{5}+3\sqrt{2})^{2} \)

To do: 

We have to simplify the given expression.

Solution:

We know that,

$(a+b)(a-b)=a^2-b^2$

$(a+b)^2=a^2+2ab+b^2$

$(a-b)^2=a^2-2ab+b^2$

Therefore,

$(2 \sqrt{5}+3 \sqrt{2})^{2}=(2 \sqrt{5})^{2}+(3 \sqrt{2})^{2}+2 \times 2 \sqrt{5} \times 3 \sqrt{2}$

$=4 \times 5+9 \times 2+2 \times 2 \times 3 \times \sqrt{5\times2}$

$=20+18+12 \sqrt{10}$

$=38+12 \sqrt{10}$

Hence, $(2\sqrt{5}+3\sqrt{2})^{2}=38+12 \sqrt{10}$.