Why are the two definitions of covariance equal?

Question

For example in Wolfram mathworld, you get these two definitions of covariance.

http://mathworld.wolfram.com/Covariance.html

cov(X,Y) = E[ (X - E[X])(Y - E[Y]) ]
= E[XY] - E[X]E[Y]

I don't see why they are equal.

Answer 1

Hint: Just expand the product indicated, then use the basic property that $$E[aX +b]= aE[X]+ b$$ if $a$ and $b$ are constants.

Remember, too, that $E[X]$ and $E[Y]$ are constants.