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

(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+1)^2(x-1)^2
=(2x)^2-(x+1)^2(x-1)^2
=(2x+(x+1)(x-1))(2x-(x+1)(x-1))
=(x^2+2x-1)(x^2+2x+1)
=(x+1)^2(x^2+2x-1)

(x+1)^4+(x^2-1)^2+(x-1)^4
=(x^4+4x^3+6x^2+4x+1)+(x^4-2x^2+1)+(x^4-4x^3+6x^2-4x+1)
=3x^4+10x^2+3

因式分解的结果是
(3x^2+1)(x^2+3)

(x+1)4+(x2-1)2+(x-1)4=4x+4+4x-2+4x-4=12x-2

12x+2