\begin{align*} \sigma^2 & = \frac{\sum_{k=1}^n ( x_k-\mu )^2}{n}\\ & = \frac{\sum_{k=1}^n ( x_k^2 - 2x_k \mu + \mu^2 )}{n}\\ & = \frac{\sum_{k=1}^n x_k^2 - 2\mu \sum_{k=1}^n x_k + n \mu^2 )}{n}\\ & = \left ( \frac{\sum_{k=1}^n x_k^2 }{n} \right ) - \mu^2 \end{align*}