Expected value with two uniformly distributed random variables A surveyor wishes to lay out a square region with each side having length L. However, because of a measurement error, he instead lays out a rectangle in which the north–south sides both have length X and the east–west sides both have length Y. Suppose that X and Y are independent and that each is uniformly distributed on the interval [L - A, L + A] (where 0 < A < L). What is the expected area of the resulting rectangle?
I tried using $E(x,y) = E(x)E(y) + Cov(x,y) = E(x)E(y)$ (since they are independent)
I ended up with $4A^2L^2$, but the answer should be just $L^2$

Hint:
If random variable $U$ is uniformly distributed over interval $[-1,1]$ then $U$ and $-U$ have the same distribution, so that  $\mathbb{E}\left(U\right)=\mathbb{E}\left(-U\right)=-\mathbb{E}\left(U\right)$ hence: $$\mathbb{E}\left(U\right)=0$$
Note that $X=L+A.U$ is uniformly distributed over interval $[L-A,L+A]$ and find its expectation making use of the linearity of expectation.
