Expected Value & Variance Question

Question

Suppose x and y are random variables such that E(xy)=0. Suppose also each of x and y has mean 2 and variance 3. Find the variance of x+y.

I understand var(x+y) = var(x) + var(y) if E(xy) = E(x)E(y)
Although, that is not the case due to 1x1 does not equal 0.
Any help would be great!

Answer 1

Hint: If $Var(X) = E(X^2) - [E(X)]^2$, then $Var(X+Y) = E[(X+Y)^2] - [E(X+Y)]^2$.

Figure out $E(X^2)$ and $E(Y^2)$ and try applying my hint making sure to use the linearity of the expectation operator.