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