x^2+y^2+z^2+xy+xz+zy
=2(x^2+y^2+z^2+xy+xz+zy)/2
=(2x^2+2y^2+2z^2+2xy+2xz+2zy)/2
=(x^2+2xy+y^2+2zy+z^2+x^2+2xz+z^2)/2
=[(x+y)^2+(y+z)^2+(x+z)^2]/2