I can get as far as:

[tex]\frac{1}{n-1}E[\displaystyle\sum ((X_i - \mu)-(\overline{X} - \mu))^2][/tex]

But my notes tell me this becomes:

[tex]\frac{1}{n-1}\displaystyle\sum E[(X_i - \mu)^2] - nE[(\overline{X} - \mu)^2][/tex]

I just don't get this step at all and gone round in circles trying to understand. Starting to lose my sanity so appreciate any help.