因式分解x3(a+1)-xy(x-y)(a-b)+y3(b+1)

Question

因式分解 x3(a+1)-xy(x-y)(a-b)+y3(b+1)

Answer 1

x3(a+1)-xy(x-y)(a-b)+y3(b+1)=ax^3+x^3-x^2y(a-b)+xy^2(a-b)+by^3+y^3=ax^3+x^3-ax^2ya+bx^2y+axy^2-bxy^2+by^3+y^3=a(x^3-x^2y+xy^2)+b(y^3+x^2y-xy^2)+x^3+y^3=ax(x^2-xy+y^2)+by(x^2-xy+y^2)+(x+y)(x^2-xy+y^2)=(ax+by+x+y)(x^2-xy+y^2)