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Expand the following:
$(\frac{2}{3} m+\frac{3}{2} n)^{2}$.
Given :
The given expression is $(\frac{2}{3} m+\frac{3}{2} n)^{2}$.
To do :
We have to expand the given expression.
Solution :
$(\frac{2}{3} m+\frac{3}{2} n)^{2}$
We know that, $(a+b)^2 = a^2 + b^2 + 2ab$
$(\frac{2}{3} m+\frac{3}{2} n)^{2} = (\frac{2}{3} m)^2 + (\frac{3}{2} n)^2 + 2(\frac{2}{3} m)(\frac{3}{2} n)$
$ = \frac{4}{9} m^2 + \frac{9}{4} n^2 + 2mn$
The expansion of $(\frac{2}{3} m+\frac{3}{2} n)^{2}$ is $\frac{4}{9} m^2 + \frac{9}{4} n^2 + 2mn$.
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