分解因式：x^3（a+1）-xy（x-y）(a-b)+y^3(b+1)
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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+y²)(b+1)+x(x²-xy+y²)(a-b)
=(x²-xy+y²)[(x+y)(b+1)+x(a-b)]
=(x²-xy+y²)(ax+x+by+y)
=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+y²)(b+1)+x(x²-xy+y²)(a-b)
=(x²-xy+y²)[(x+y)(b+1)+x(a-b)]
=(x²-xy+y²)(ax+x+by+y)
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