How do you factor  9y^2 - 1 ?

$9 {y}^{2} - 1 = \left(3 y + 1\right) \left(3 y - 1\right)$
$9 {y}^{2} - 1$
$= {\left(3 y\right)}^{2} - {\left(1\right)}^{2}$
Using the identity ${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right) ,$
You can further simplify $\left({\left(3 y\right)}^{2} - {\left(1\right)}^{2}\right)$ as
${\left(3 y\right)}^{2} - {\left(1\right)}^{2} = \left(3 y + 1\right) \left(3 y - 1\right)$