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已知x^3=10-y^3,x^2y-xy^2=-3,求代数式（x^3-y^3）-(2x^y-4xy^2)-2(-y^3+xy^2)的值
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已知x^3=10-y^3,x^2y-xy^2=-3,求代数式（x^3-y^3）-(2x^y-4xy^2)-2(-y^3+xy^2)的值
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答案和解析
x^3=10-y^3,x^2y-xy^2=-3
则x^3+y^3=10,x^2y-xy^2=-3
（x^3-y^3）-(2x^y-4xy^2)-2(-y^3+xy^2)
=x^3-y^3-2x^y+4xy^2+2y^3-2xy^2
=x^3+y^3-2x^y+2xy^2
=(x^3+y^3)-2(x^y-xy^2)
=10+6
=16
则x^3+y^3=10,x^2y-xy^2=-3
（x^3-y^3）-(2x^y-4xy^2)-2(-y^3+xy^2)
=x^3-y^3-2x^y+4xy^2+2y^3-2xy^2
=x^3+y^3-2x^y+2xy^2
=(x^3+y^3)-2(x^y-xy^2)
=10+6
=16
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