Answer
$= \frac{23}{36}$
Work Step by Step
We plug in $x = \frac{1}{2}$ and $y= -\frac{1}{3}$ to obtain:
$= 3x^{2} - y^{2}$
$= 3(\frac{1}{2})^{2} - (-\frac{1}{3})^{2}$
$= 3(\frac{1}{4}) -\frac{1}{9}$
$= \frac{3}{4} - \frac{1}{9} $
$=\frac{27}{36} - \frac{4}{36}$
$= \frac{23}{36}$
