Question

求一道因式分解题目的解题过程

(x+1)4+(x2-1)2+(x-1)4=

Answer 1

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