My motivation for this question is the following question posted here: Variance of Sample Variance
I understood the computations and the math operations, but I'm trying to understand why, assuming that $Z_i = X_i -\mu$ $$S^2_n = \dfrac{n\sum_{i=1}^{n} X_i^2 - (\sum_{i=1}^{n} X_i)^2}{n(n-1)} = \dfrac{n\sum_{i=1}^{n} Z_i^2 - (\sum_{i=1}^{n} Z_i)^2}{n(n-1)}$$
