Basically I have to prove that the sample variance of a sample is given by:

$\displaystyle s^2 =$ $\displaystyle {\sum_{j=1}^nx_j^2-{1\over n}}(\sum_{j=1}^nx_j)^2\over n-1}$

For my purposes it's sufficient to show that $\displaystyle {\sum_{j=1}^n(x_j-x_j^2) = {\sum_{j=1}^nx_j^2-{1\over n}}(\sum_{j=1}^nx_j)^2$

Help is appreciated. Thanks in advance.

If I made any mistakes inputting the sums please let me know.