How do you transform equation 1 to equation 2? (equations given below)?

Question

immediate help needed!

Equation 1: [Σ(x - M)^2]/N
Equation 2: [ Σx^2 - (((Σx)^2)/N)]
M = (Σx)/N

both equations are the equations for variance (stats).
thanks!

Answer 1

Just put your head down and plow ahead. (X-M)^2 has three terms. So its sum can be broken out as the sum of three summations.

Hint: Calling your desired answer A - B, one of your intermediate steps in the proof will be A - 2B + B.

Answer 2

If you square equation 1 you get [sum(x^2)-sum(2xM)+sum(M^2)]/n. This simplifies to sum(x^2)/n -2Msum(x)/n+sum(M^2)/n
The middle term is just -2M^2, since M=sum(x)/n, and the last term is M^2. Therefore, the whole thing simplifies to [sum(x^2)/n -M^2] which easily simplifies to 1.