let $\displaystyle E(X)=\mu$ and $\displaystyle Var(X)=\sigma^2$
Show that $\displaystyle E[X(X-1)] = \mu(\mu-1)+\sigma^2$
$\displaystyle Var(x)=E((X-\mu)^2)=E(X^2-2\mu X+\mu ^2)$
$\displaystyle =E(X^2)-2\mu E(X)+\mu ^2$
$\displaystyle =E(X^2)-2\mu ^2 + \mu ^2 = E(X^2)-\mu ^2$
So we have $\displaystyle E(X^2)=Var(x)+\mu ^2$
You should be able to use this last line to help you in your proof. Can you take it from here?