In the first problem set problem 1F-2 I got the same answer as the left side of the equation in the answer key, but I can't figure out how it simplifies to what's on the right side. Did anybody follow the algebra better than I did?

Question

In the first problem set problem 1F-2 I got the same answer as the left side of the equation in the answer key, but I can't figure out how it simplifies to what's on the right side.  Did anybody follow the algebra better than I did?

anonymous · Answer

Sure, notice that you can take $$(x^2+1)^9$$ as a common factor like this: $$(x^2+1)^{10} = (x^2+1)^9 * (x^2+1)$$
Also, $$(x^{10})*10*2x$$ can be written as $$10x^9 * 2x^2$$ thus making $$10x^9$$ a common factor. After taking those two common factors just sum up everything that's left inside.