Question

How do you factor (x^2+1)^(1/2)*(x^2-1)+((x^2+1)^(3))^(1/2)*(2x^2-2)?

Answer 1

(x^2+1)^(1/2) and (x^2-1) are factors of both of the added terms. Bring them outside as factors and you have

[(x^2+1)^(1/2)*(x^2-1)]*
[x^2+1 + 2(x^2-1)]
= [(x^2+1)^(1/2)*(x^2-1)]*
[3x^2 -1]

This is not a calculus question.

If you want to factor it some more, you could replace x^2-1 with (x+1)(x-1)