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Algebra in a Calculus Problem - Finding the Second Derivative of a Function

How did the book get from here:

-2X(1+x^2)^2 - 4X(1-x^2)(1+x^2)
(1 + x^2)^4

to here?

-2x (1+ x^2)[1+x^2+2(1-x^2]

I have worked and reworked and I cannot get that numerator to become that. What is the deal?

(This is in the middle of trying to find the second derivative of a function, although I don't believe that should make a difference as I am still plowing through the algebra here)