\begin{eqnarray*} Cov[X, Y] & = & E[(X-EX)(Y-EY)] \\ & = & E[XY] - (EX)(EY) \\ \end{eqnarray*}

\begin{eqnarray*} E[(X−EX)(Y−EY)] & = & E[XY−X(EY)−(EX)Y+(EX)(EY)] \\ & = & E[XY]−(EX)(EY)−(EX)(EY)+(EX)(EY) \\ & = & E[XY]−(EX)(EY)\\ \end{eqnarray*}