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}

と一行付け足せば分かるか？