# How do you factor 36g^2-49h^2?

Jun 11, 2016

$36 {g}^{2} - 49 {h}^{2} = \left(6 g + 7 h\right) \left(6 g - 7 h\right)$

#### Explanation:

The difference of squares formula states that

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

(Try expanding the right hand side to verify this)

Using that, we have

$36 {g}^{2} - 49 {h}^{2}$

$= {\left(6 g\right)}^{2} - {\left(7 h\right)}^{2}$

$= \left(6 g + 7 h\right) \left(6 g - 7 h\right)$