in the third step, why does the x^4 change to x^2?, distributing divides the power in half?
It doesn't, it's been changed to $\displaystyle \displaystyle \begin{align*} x^2 \cdot x^2 \end{align*}$. It does this so you can divide each term in each of the factors by $\displaystyle \displaystyle \begin{align*} x^2 \end{align*}$.