Answer
$= -\frac{73}{18}$
Work Step by Step
We plug in $x =- \frac{2}{3}$ and $y= \frac{3}{2}$ to obtain:
$= x^{2} - 2y^{2}$
$= (-\frac{2}{3})^{2} - 2(\frac{3}{2})^{2}$
$= (\frac{4}{9}) - 2(\frac{9}{4})$
$= (\frac{4}{9}) - (\frac{18}{4})\\\\=\frac{16}{36}-\frac{162}{36}$
$= -\frac{73}{18}$
