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

题目

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

答案

∵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