I need some help with algebra now.

x^4 - 1 + x^4 - x^2
factorize this eqn
pls include the steps taken to get the answer :-)

btw the answer is (x-1)(x+1)(2x^2-1)

x^4 - 1 + x^4 - x^2
(x^4 - 1) + (x^4 - x^2)
(x^2-1)(x^2+1) + x^2(x^2-1)
(x^2-1)[x^2+1+x^2]
(x^2-1)(2x^2+1)
(x-1)(x+1)(2x^2+1)