一道因式分解的难题因式分解（1+y)^2-2x^2(1+y^2)+x^4(1-y)^2

一道因式分解的难题因式分解（1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
一道因式分解的难题
因式分解（1+y)^2-2x^2(1+y^2)+x^4(1-y)^2

一道因式分解的难题因式分解（1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
=(1+y)^2+2(1+y)x^2(1+y)+x^4(1-y)^2-2(1+y)x^2(1-y)-2x^2(1+y^2)
=[(1+y)+x^2(1-y)]^2-2(1+y)x^2(1-y)-2x^2(1+y^2)
=[(1+y)+x^2(1-y)]^2-(2x)^2
=[(1+y)+x^2(1-y)+2x]·[(1+y)+x^2(1-y)-2x]
=(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1)
=[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)]
=(x+1)(x+1-xy+y)(x-1)(x-1-xy-y)

((1+y)-x∧2(1-y))∧2-4x∧2y∧2
=((1+y)-x∧2(1-y)-2xy)((1+y)-x∧2(1-y)+2xy)
貌似是这样的，接下来就自己整理一下

因为（1-Y)^2*(-1)+1*[-(1+Y)^2=-2(1+Y)^2
所以(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2
=[(1-Y)^2X^2-(1+Y)^2](x^2-1)
=[(1-Y)X+(1+Y)][(1-Y)X-(1+Y)](X+1)(X-1)
=(X+1-XY+Y)(X-1-XY-Y)(x+1)(X-1)