(1+y)^2-2x^2(1-y^2)+x^4(1-y)^2因式分解
问题描述：
(1+y)^2-2x^2(1-y^2)+x^4(1-y)^2因式分解
答
(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