# How do you factor 0.09y^2 - 0.81?

Nov 30, 2015

$0.09 {y}^{2} - 0.81 = \left(0.3 y + 0.9\right) \left(0.3 y - 0.9\right)$

#### Explanation:

The difference of squares formula gives us
${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$
(you can multiply this out to confirm)

$0.09 {y}^{2} = {\left(0.3 y\right)}^{2}$
and
$0.81 = {0.9}^{2}$

Thus, by the difference of squares formula

$0.09 {y}^{2} - 0.81 = \left(0.3 y + 0.9\right) \left(0.3 y - 0.9\right)$