I have this equation:
$$-\frac{n-1}{n-2}\left\{ \frac{b\sum_{i=1}^{n}x_i^2\left[ x_i^2-\left( \frac{\sum_{j=1}^{n}x_j^2}{n}\right)\right]}{\left( \sum_{i=1}^{n}x_i^2 \right)^2} \right\} [1]$$
and he transforms it into: $$-\frac{n-1}{n-2}\left\{\frac{b\sum_{i=1}^{n}\left[x_i^2-\frac{\sum_{j=1}^{2}x_j^2}{n}\right]\left[x_i^2-\frac{\sum_{j=1}^{2}x_j^2}{n}\right]}{\left(\sum_{i=1}^{n}x_i^2\right)^2} \right\} +\frac{n-1}{n-2}\left\{\frac{\frac{b*\sum_{j=1}^{n}x_j^2}{n}\sum_{i=1}^{n}\left(x_i^2-\frac{\sum_{j=1}^{n}x_j^2}{n}\right)}{\left(\sum_{i=1}^{n}x_i^2\right)^2}\right\} [2]$$
I do not understand why equation [1] is equal to equation [2]. Also, how can someone come up with this. I would have never thought of doing this in an exam if that equation would have been given to me for the first time? Should I just memorize the process of doing this? I mean in an exam I don't have a few hours to just try and see what works. (this equation is part of demonstrating that that that the expected value of a term understimate the variance of another term)