因式分解:x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)
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因式分解:x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)
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![因式分解:x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)](/uploads/image/z/719931-3-1.jpg?t=%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%3Ax%5E3%28a%2B1%29-xy%28x-y%29%28a-b%29%2By%5E3%28b%2B1%29)
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)
=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)
因式分解:x^3(a+1)-xy(x-y)(a-b)+y^3(b+1)
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