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 $\frac{4}{9} m^2 + \frac{9}{4} n^2 + 2mn$.