how to understand xy - XY (Where x, y are random variables and XY are their means)

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Part where I don't understand

Hey guys,

I'm just looking at this paper called: ON THE EXACT VARIANCE OF PRODUCTS. http://www.cs.cmu.edu/~cga/var/2281592.pdf

I'm a bit confused in the second section :
2.THE CASE WHERE THE RANDOM VARIABLES ARE INDEPENDENT

Where it says:

Since xy - XY = XY[(dx + l)(dy + 1) - 1] = XY[dy + dx + dxdy](1)
where dx = (x - X)/X and dy = (y - Y)/ Y 

x,y here are both random variables, and X,Y are E(x) and E(y), their respective means.

How does one get to the equation in (1), and why the choice for dx and dy here?

Thanks a lot in advance!