Let X and Y be random variables.
$$Cov[X, Y]=E[XY]-E[X]E[Y]$$
Proof
\begin{eqnarray*}Cov[X, Y]&=&E[(X-E[X])(Y-E[Y])]\\&=&E[XY–XE[Y]-E[X]Y+E[X]E[Y]]\\&=&E[XY]-E[X]E[Y]-E[X]E[Y]+E[X]E[Y]\ \ \ (\ \text{∵}\ E[aX]=aE[X] \ )\\&=&E[XY]-E[X]E[Y]\end{eqnarray*}