Generated by the Physics Derivation Graph. Eq. \ref{eq:3493498} is an identity. \begin{equation} \langle \left(x-\langle x \rangle\right)^2 \rangle = \langle x^2 \rangle-\langle x \rangle^2 \label{eq:3493498} \end{equation} Simplify Eq. \ref{eq:3493498}; yields Eq. \ref{eq:5049530}. \begin{equation} \langle x^2 - 2 x \langle x \rangle + \langle x \rangle^2 \rangle = \langle x^2 \rangle-\langle x \rangle^2 \label{eq:5049530} \end{equation} Simplify Eq. \ref{eq:5049530}; yields Eq. \ref{eq:6757584}. \begin{equation} \langle x^2\rangle -2\langle x \rangle\langle x \rangle+\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2 \label{eq:6757584} \end{equation} Simplify Eq. \ref{eq:6757584}; yields Eq. \ref{eq:3294824}. \begin{equation} \langle x^2\rangle -2\langle x^2 \rangle+\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2 \label{eq:3294824} \end{equation} Simplify Eq. \ref{eq:3294824}; yields Eq. \ref{eq:5949484}. \begin{equation} \langle x^2\rangle -\langle x \rangle^2 = \langle x^2 \rangle-\langle x \rangle^2 \label{eq:5949484} \end{equation} Thus we see that LHS of Eq. \ref{eq:5949484} is equal to RHS.