Question

(1+y)^2-2x^2(1-y^2)+x^4(1-y)^2因式分解

Answer 1

(1+y)^2-2x^2(1-y^2)+x^4(1-y)^2

=(1+y)²-2x²(1+y)(1-y)+[x²(1-y)]²

=[(1+y) - x²(1-y)]²

=(1+y-x²+x²y)²

令 1+y=a ,x²(1-y)=b

原式

=(1+y)²-2x²(1+y)(1-y)+[x²(1-y)]²

=a²-2ab+b²

=(a-b)²

=[(1+y) - x²(1-y)]²

=(1+y-x²+x²y)²