神马作文网试证明(x^3+3x^2y-2xy^2+1)+(x^3-4x^2y+3xy^2-10)+(-xy^2+x^2y-2x^3
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/11/18 16:02:51
试证明(x^3+3x^2y-2xy^2+1)+(x^3-4x^2y+3xy^2-10)+(-xy^2+x^2y-2x^3+3)的值与x,y无关
(x^3+3x^2y-2xy^2+1)+(x^3-4x^2y+3xy^2-10)+(-xy^2+x^2y-2x^3+3)
=x^3+3x^2y-2xy^2+1+x^3-4x^2y+3xy^2-10-xy^2+x^2y-2x^3+3
=x^3+x^3-2x^3+3x^2y+x^2y-4x^2y+3xy^2-2xy^2-xy^2+3+1-10
=3+1-10
=-6
所以(x^3+3x^2y-2xy^2+1)+(x^3-4x^2y+3xy^2-10)+(-xy^2+x^2y-2x^3+3)的值与x,y无关
=x^3+3x^2y-2xy^2+1+x^3-4x^2y+3xy^2-10-xy^2+x^2y-2x^3+3
=x^3+x^3-2x^3+3x^2y+x^2y-4x^2y+3xy^2-2xy^2-xy^2+3+1-10
=3+1-10
=-6
所以(x^3+3x^2y-2xy^2+1)+(x^3-4x^2y+3xy^2-10)+(-xy^2+x^2y-2x^3+3)的值与x,y无关
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