Simplify
Question:

Simplify $(2 \sqrt{5}+3 \sqrt{2})^{2}$.

 

Solution:

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

$=(2 \sqrt{5})^{2}+(3 \sqrt{2})^{2}+2(2 \sqrt{5})(3 \sqrt{2}) \quad\left[(a+b)^{2}=a^{2}+b^{2}+2 a b\right]$

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

$=38+12 \sqrt{10}$

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