Rewriting Sample Variance Formula

Question

Why can $s^2 = \frac{\sum_{i=1}^{n}{(X_i - \bar{X})^2}}{n-1}$ be written as $ s^2 = \frac{\sum_{i=1}^{n}{X_i^2 - n(\bar{X})^2}}{n-1} $?

Answer 1

$$\sum_{i=1}^n(X_i - \bar{X}_n)^2 = \sum_{i=1}^n\left( X_i^2 - 2X_i\bar{X}_n + \bar{X}_n^2\right)=\sum X_i^2 -2\bar{X}_n\sum X_i + \sum\bar{X}_n^2,$$ Now, recall that $\sum X_i =n\bar{X}_n$ and $\sum\bar{X}_n^2=n\bar{X}_n^2$, hence $$ \sum_{i=1}^n(X_i - \bar{X}_n)^2 = \sum X_i^2 - n \bar{X}_n^2. $$