Explaining the Summation Process

Question

So I have two separate summations, with the only difference being the first variable being squared in the second one. Can somebody explain to me how they got from the second to the third step on both. I don't see how this is occurring.

Answer 1

You can just insert the values for $y_1$. In the first case this yields $3p(1-p)^2+6p^2(1-p)+3p^3=3p(1-2p+p^2)+6p^2-6p^3+3p^3=3p-6p^2+3p^3+6p^2-6p^3+3p^3=3p$. The second one can be obtained analogously.