Answer
$2(x+y+z)$
Work Step by Step
div $\textbf{F}=\nabla \cdot \textbf{F}=\nabla\cdot\langle x^{2}-y^{2},y^{2}-z^{2},z^{2}-x^{2}\rangle$
$=\frac{\partial}{\partial x}(x^{2}-y^{2})+\frac{\partial}{\partial y}(y^{2}-z^{2})+\frac{\partial}{\partial z}(z^{2}-x^{2})$
$=(2x-0)+(2y-0)+(2z-0)=2(x+y+z)$
