How was this principal normal vector equation simplified?

Question

I can't seem to figure out what to do.

$$T'(t)=-\frac{1}{2}(4t^2+1)^{-3/2}8t(2t{i}+{j})+(4t^2+1)^{-1/2}2{i} = 2(4t^2+1)^{-3/2}\big({i}-2t{j}\big)$$

I don't understand how half the equation seems to just disappear.

Answer 1

\begin{equation} \label{eq1} \begin{split} T'(t)&=-\frac{1}{2}(4t^2+1)^{-3/2}8t(2t{i}+{j})+(4t^2+1)^{-1/2}2{i} \\ & = -\frac{1}{2}(4t^2+1)^{-3/2}8t(2t{i}+{j})+(4t^2+1)(4t^2+1)^{-3/2}2{i}\\ & = (4t^2+1)^{-3/2}\big(-4t(2t{i}+{j})+(4t^2+1)2{i}\big) \\ & = (4t^2+1)^{-3/2}\big(-8t^2{i}-4t{j}+8t^2{i}+2{i}\big) \\ & = (4t^2+1)^{-3/2}\big(-4t{j}+2{i}\big) \\ & = 2(4t^2+1)^{-3/2}\big({i}-2t{j}\big) \end{split} \end{equation}