Classical Electrodynamics by Jackson says
"With a Taylor series expansion of the well-behaved $\rho (\mathbf{x'})$ around $\mathbf{x'} = \mathbf{x}$ one finds ..."
and then he says basically that
$\rho (\mathbf{x'}) = \rho (\mathbf{x}) + \frac{r^2}{6}\nabla^2\rho + \ldots$
above, note that $ r = |\mathbf{x'} -\mathbf{x}|$ and we are in $3$ dimensions
Could someone explain how to derive this Taylor series result for a function of a vector? I've never seen this before and am at a loss.
UPDATE:
Perhaps the trick is to notice $\mathbf{x'} = \mathbf{x} -\mathbf{r}$ and then do some sort of expansion about $r = 0$?