\begin{gather*} = n(n-1)p^2 \sum_{k=0}^{m} {\frac{m!}{k!(m-k)!} p^k (1-p)^{m-k}} + np - n^2p^2\\ = n(n-1)p^2 + np - n^2p^2 = np - np^2 = np(1-p) \end{gather*}