# How do you factor 6x^2-21?

Sep 2, 2016

$6 {x}^{2} - 21 = 3 \left(\sqrt{2} x - \sqrt{7}\right) \left(\sqrt{2} x + \sqrt{7}\right)$

#### Explanation:

The difference of squares identity can be written:

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

We use this with $a = \sqrt{2} x$ and $b = \sqrt{7}$ as follows:

$6 {x}^{2} - 21 = 3 \left(2 {x}^{2} - 7\right)$

$\textcolor{w h i t e}{6 {x}^{2} - 21} = 3 \left({\left(\sqrt{2} x\right)}^{2} - {\left(\sqrt{7}\right)}^{2}\right)$

$\textcolor{w h i t e}{6 {x}^{2} - 21} = 3 \left(\sqrt{2} x - \sqrt{7}\right) \left(\sqrt{2} x + \sqrt{7}\right)$