x^3(a+1)-xy(x-y)(a-b)+y3^(b+1) 因式分解
问题描述：
x^3(a+1)-xy(x-y)(a-b)+y3^(b+1) 因式分解
答
x^3(a+1)-xy(x-y)(a-b)+y3^(b+1)
=x^3(a+1)-(x^2y-xy^2)(a-b)+y^3(b+1)
=x^3(a+1)-(x^2y-xy^2)a+(x^2y-xy^2)b+y^3(b+1)
=a(x^3-x^2y+xy^2)+b(x^2y-xy^2+y^3)+x^3+y^3
=ax(x^2-xy+y^2)+by(x^2-xy+y^2)+(x+y)(x^2-xy+y^2)
=(x^2-xy+y^2)(ax+by+x+y)
答
x³(a+1)-xy(x-y)(a-b)+y³(b+1)=x³(a-b+b+1)-xy(x-y)(a-b)+y³(b+1)=x³(a-b)+x³(b+1)-xy(x-y)(a-b)+y³(b+1)=(x³+y³)(b+1)+[x³-xy(x-y)](a-b)=(x+y)(x²-xy+y...