已知x-y=4,y-z=2,求x^2y+y^2z+z^2x-(xy^2+yz^2+zx^2)的值

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已知x-y=4,y-z=2,求x^2y+y^2z+z^2x-(xy^2+yz^2+zx^2)的值
已知x-y=4,y-z=2,求x^2y+y^2z+z^2x-(xy^2+yz^2+zx^2)的值

已知x-y=4,y-z=2,求x^2y+y^2z+z^2x-(xy^2+yz^2+zx^2)的值
∵x-y=4,y-z=2,∴x-z=6
∴x^2y+y^2z+z^2x-(xy^2+yz^2+zx^2)
=(x^2y-xy^2)+(y^2z-yz^2)+(z^2x-zx^2)
=xy(x-y)+yz(y-z)+xz(z-x)
=4xy+2yz-6xz
=(4xy-4xz)+(2yz-2xz)
=4x(y-z)+2z(y-x)
=8x-8z
=8(x-z)
=48

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