Question

1．分解因式(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2

Answer 1

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)