Title says it all: if $X$ is a $\pm 1$-valued random variable with mean $\mu$, 'why' is $\mathbf{E}[|X - \mu|] = \mathbf{E}[|X-\mu|^2]$? Obviously one can do a couple of lines of trivial algebra to verify it, but is there a simple-to-state reason? Something you can say to make me say, "Oh yeah, of course" without any calculation?
Thanks!