Value of E(XY), dependant variables?

Question

Let $A_1, A_2, A_3$ be independent variables.

Let $X=2A_2-A_1$ and $Y=A_3+3A_1$

How can I calculate $E(XY)=E[(2A_2-A_1)(A_3+3A_1)]$?

NOTE: I can calculate each $EA_n$ separately: $EA_1=0.5, EA_2=0, EA_3=2$

The final question is about covariance, but this is where I got stuck.

Answer 1

$E(XY)=E[(2A_2-A_1)(A_3+3A_1)]=E[2A_2A_3+6A_1A_2-A_1A_3-3A_1^2]$

=$E(2A_2A_3)+E(6A_1A_2)+E(-A_1A_3)+E(3A_1^2)$

$=2E(A_2)E(A_3)+6E(A_1)E(A_2)-E(A_1)E(A_3)-3(V(A_1)+E(A_1)^2)$

I used the rules for splitting up the expectation of a sum(here we do not use independence). But then I used independence for instance when $E(A_2A_3)=E(A_2)E(A_3)$ etc. And last you use that $V(A_1)=E(A_1^2)-E(A_1)^2$.