Show that for $\forall x,y,z \in \mathbb{R},x^2+y^2+z^2\geq xy+yz+xz $.

I first assumed that $x\geq y \geq z$, but I'm having problems with the $z^2$. By itself, $z^2$ is clearly not greater than any of products of the other terms so I tried to show that $z^2+y^2$ was greater than something but failed. Can someone explain how I could prove this?