(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2 (可用添拆项法) 分解因式_数学解答

(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2 (可用添拆项法) 分解因式

人气：137 ℃　时间：2020-08-08 20:42:14

解答

原式=[(1+y)-x^2(1-y)]^2-4*x^2*y^2
=(1+y-x^2+x^2*y)^2-(2xy)^2
=(1+y+2xy-x^2+x^2*y)(1+y-2xy-x^2+x^2*y)
=[(1-x^2)+(yx+y)+(x^2*y+xy)][(1-x^2)-(xy-y)+(x^2*y-xy)]
=(x+1)(x-1)(x-xy+1+y)(x-xy-1-y)