Answer
$\text{area} = (x-y)(x+y)$
Work Step by Step
The area of the shaded region is equal to the difference between the areas of the bigger square and the smaller square.
Thus, the area of the shaded region is:
$A=\text{area of the bigger square}-\text{area of the smaller square}
\\A=x(x) - y(y)
\\A=x^2-y^2$
RECALL: $a^2-b^2=(a-b)(a+b)$
Use the formula above where $a=x$ and $b=y$ to have:
$\\A=x^2-y^2=(x-y)(x+y)$
