因式分解x3+x2+xy-xy2

题目

因式分解x3+x2+xy-xy2

答案

x^3+x^2+xy-xy^2
=x(x^2+x+y-y^2)
=x(x^2-y^2+x+y)
=x[(x+y)(x-y)+(x+y)]
=x(x+y)(x-y+1)