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?

Answer 1

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.