Answer
$-2x^2-2y^2$
Work Step by Step
$\frac{1}{2}x^2-\frac{1}{2}y^2-\frac{5}{2}x^2+\frac{5}{2}y^2$
First, you must combine the like terms.
The like terms are
$\frac{1}{2}x^2-\frac{5}{2}x^2$
and
$-\frac{1}{2}y^2+\frac{5}{2}y^2$.
Then you add them together to get
$-\frac{4}{2}x^2$, which simplifies to $-2x^2$,
and
$-\frac{4}{2}y^2$, which simplifies to $-2y^2$.
Therefore, your final answer is $-2x^2-2y^2$
