# How do you factor 5y^2-90?

Apr 18, 2016

$5 {y}^{2} - 90 = 5 \left(y - 3 \sqrt{2}\right) \left(y + 3 \sqrt{2}\right)$

#### Explanation:

Separate out the common scalar factor $5$, express as a difference of squares, then use the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

with $a = y$ and $b = 3 \sqrt{2}$ as follows:

$5 {y}^{2} - 90$

$= 5 \left({y}^{2} - 18\right)$

$= 5 \left({y}^{2} - {3}^{2} \cdot 2\right)$

$= 5 \left({y}^{2} - {\left(3 \sqrt{2}\right)}^{2}\right)$

$= 5 \left(y - 3 \sqrt{2}\right) \left(y + 3 \sqrt{2}\right)$