不论X,Y取何值代数式(X^3Y+3X^2Y-5XY^2+6Y^3)+(Y^3+2XY^2+X^2Y-2X^3)-(4X
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/22 07:53:58
不论X,Y取何值代数式(X^3Y+3X^2Y-5XY^2+6Y^3)+(Y^3+2XY^2+X^2Y-2X^3)-(4X^2Y-X^3-3XY^2+7Y^3)的值是常数
(X^3+3X^2Y-5XY^2+6Y^3)+(Y^3+2XY^2+X^2Y-2X^3)-(4X^2Y-X^3-3XY^2+7Y^3)
=X^3+3X^2Y-5XY^2+6Y^3+Y^3+2XY^2+X^2Y-2X^3-4X^2Y+X^3+3XY^2-7Y^3
=(X^3-2X^3+X^3)+(3X^2Y+X^2Y-4X^2Y)+(-5XY^2+2XY^2+3XY^2)+(6Y^3+Y^3-7Y^3)
=0+0+0+0
=0
所以值是常数
=X^3+3X^2Y-5XY^2+6Y^3+Y^3+2XY^2+X^2Y-2X^3-4X^2Y+X^3+3XY^2-7Y^3
=(X^3-2X^3+X^3)+(3X^2Y+X^2Y-4X^2Y)+(-5XY^2+2XY^2+3XY^2)+(6Y^3+Y^3-7Y^3)
=0+0+0+0
=0
所以值是常数
不论X,Y取何值代数式(X^3Y+3X^2Y-5XY^2+6Y^3)+(Y^3+2XY^2+X^2Y-2X^3)-(4X
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[x(x^2y^2-xy)-y(x^2-x^3y)]/3x^2y