Change of Variables & the Jacobian · Hard problem

Let $R$ be the region bounded by the lines $x + y = 1$, $x + y = 3$, $x - y = 0$ and $x - y = 2$. Use the substitution $u = x + y$, $v = x - y$ to evaluate $\displaystyle\iint_R (x + y)(x - y)^2\,dA$.