Tensor notation in vectors

Question

I have the following expression

$\partial_{x_a}(\partial_{x_b} \rho \partial_{x_b}\rho) - \partial_{x_b}(\partial_{x_a}\rho\partial_{x_b}\rho)$

How do I write this in vector notation? At least the first term will be (I think, at least...)

$\nabla \cdot |\nabla\rho|^2$

Thanks in advance.