已知x-y=m,y-z=n,要求出x^2+y^2+z^2-xy-yz-zx

x=y+m,z=y-n
原式=(y+m)^2+y^2+(y-n)^2-（y+m)y-(y-n)y-(y+m)(y-n)
=y^2+2my+m^2+y^2+Y^2-2ny+n^2-Y^2-ym-y^2+ny-y^2-my+ny+mn
y^2、2my、2ny均可约去,
原式=m^2+n^2+mn