Hello ! I have trouble getting to the end of this exercise :

Y1 et Y2 are two random variables following Poisson distributions with parameters y1 et y2.

U = Y1 + Y2 et V = aY1 - aY2 with a ≠ 0

Give the value of the covariance of U and V

I started with Cov (U,V)= E(UV) - E(U)E(V) = E((Y1 + Y2)a(Y1-Y2)) - E(Y1+Y2) aE(Y1-Y2))

I know the end result to be obtained is cov(U,V)=a(var(Y_{1})-var(Y_{2})). However I don't see how to proceed to get to this form, I tried to develop the expression but ended up with nonsense.

Thank you for your help !