化简:x^3-x^2y+xy^2+yx^2+y^2x+y^3其中X=-1,Y=-1/2,Z=-1/3,求值错了错了..x=3/2...y=-4/3

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化简:x^3-x^2y+xy^2+yx^2+y^2x+y^3其中X=-1,Y=-1/2,Z=-1/3,求值错了错了..x=3/2...y=-4/3
化简:x^3-x^2y+xy^2+yx^2+y^2x+y^3
其中X=-1,Y=-1/2,Z=-1/3,求值
错了错了..x=3/2...y=-4/3

化简:x^3-x^2y+xy^2+yx^2+y^2x+y^3其中X=-1,Y=-1/2,Z=-1/3,求值错了错了..x=3/2...y=-4/3
你写错没有哦,没有z啊
就带值进去算还简单些
原式=（x^3+y^3）+（xy^2+yx^2）+y^2x-x^2y
=(x+y)(x^2-xy+y^2)+xy(y+x)+y^2x-x^2y
=(x+y)(x^2+y^2)+y^2x-x^2y
带值=（-1-1/2）*(1+1/4)+4-1
=9/8

x^3-x^2y+xy^2+yx^2-y^2x+y^3
=x(x^2-xy+y^2)+y(x^2-yx+y^2)
=(x+y)(x^2-xy+y^2)
=(x+y)[(x-y)^2+xy]
=(1/6)*[(17/6)^2-2]
=217/216
x+y=3/2+(-4/3)=1/6
x-y=3/2-(-4/3)=17/6

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x^3-x^2y+xy^2+yx^2-y^2x+y^3
=x(x^2-xy+y^2)+y(x^2-yx+y^2)
=(x+y)(x^2-xy+y^2)
=(x+y)[(x-y)^2+xy]
=(1/6)*[(17/6)^2-2]
=217/216
x+y=3/2+(-4/3)=1/6
x-y=3/2-(-4/3)=17/6
xy=3/2*(-4/3)=-2
x^2yz-x^4+1/2x^2y^2-1/6x^2y^2+x^4-1/2x^2y^2
=x^2yz-1/6x^2y^2
=x^2y(z-1/6y)
=1*(-2)*(-1/3+1/3)=0

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