Change of Variables & the Jacobian · Medium problem

Let $R$ be the square with vertices $(2,0)$, $(0,2)$, $(-2,0)$, $(0,-2)$ (so $|x+y|\le2$ and $|x-y|\le2$). Using the substitution $u=x+y$, $v=x-y$, evaluate $\displaystyle\iint_R (x+y)^2\,dA$.