Statistics maths problem please helppppppp? :(

I need the sol. for this proof asap

proof that:

n n
Σ (Yi - Ῡ)² = Σ (Yi)² - n(Ῡ)²
ἰ=1 ἰ=1



thanks.

Σ (Yi - Ῡ)² = Σ(Yi^2 - 2*Yi*Ῡ + Ῡ^2) = Σ(Yi^2) - 2*Ῡ*ΣYi + ΣῩ^2 =

- 2*Ῡ*ΣYi, multiply and divide by n

- 2*n*Ῡ*ΣYi/n = - 2*n*Ῡ*Ῡ = - 2*n*Ῡ^2

ΣῩ^2 = n*Ῡ^2, because it's the sum of a constant!

Σ(Yi^2) - 2*Ῡ*ΣYi + ΣῩ^2 = Σ(Yi^2) - 2*n*Ῡ^2 + n*Ῡ^2 = Σ(Yi^2) - n*Ῡ^2, done!