This simplification came directly from my book. I think it is wrong, but I may just not understand it fully. Here it is:

$\displaystyle T'(t) = \\-4t(2t^2 + 1)^-2 <2t,2t^2,1> +\\ (2t^2 +1)^-1 <2,4t,0> \\ = (2t^2 + 1)^-2 <-8t^2 + 4t^2 + 2, \\-8t^3 + 8t^3 + 4t, -4t> \\ = 2(2t^2 + 1)^-2 <1-2t^2, 2t, -2t>$

I don't understand how they factored out the (2t^2 + 1)^-2. Is it wrong, or am I just missing something? Thanks.