因式分解:x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)

x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)
=ax^3+x^3-ayx^2+byx^2+axy^2-bxy^2+by^3+y^3
=ax(x^2-xy+y^2)+by(x^2-xy+y^2)+(x+y)(x^2-xy+y^2)
=〔(a+1)x+(b+1)y〕(x^2-xy+y^2)