How do you factor -9r^2 + 81?

$= - 9 \left(r - 3\right) \left(r + 3\right)$
The difference of squares rule states that: ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$, and using this:
$- 9 {r}^{2} + 81 = - 9 \left({r}^{2} - 9\right)$
$= - 9 \left({r}^{2} - {3}^{2}\right)$
$= - 9 \left(r - 3\right) \left(r + 3\right)$