(x^2+y^2+z^2-xy-yz-zx)

=(1/2)*(2x^2+2y^2+2z^2-2xy-2yz-2zx)

=(1/2)*(x^2-2xy+y^2 + y^2-2yz+z^2 + z^2-2zx+x^2)

=(1/2)*{(x-y)^2+(y-z)^2+(z-x)^2}