Mental Workouts

I have decided to stem my mental atophy by doing the of occasional mental push ups. Today, I tried to prove that \Sigma^N_{i=1}(x_i - \tilde x)^2 = \Sigma^N_{i=1}(x_i ^2- \tilde x^2)

I feel proud of myself. I intend to work out these algebraic problems occasionally (perhaps throw in some indefinite integrals for fun), so that I keep my brain nimble.