# How do you factor (x^2-5)?

Oct 29, 2015

${x}^{2} - 5 = \left(x - \sqrt{5}\right) \left(x + \sqrt{5}\right)$

#### Explanation:

The difference of squares identity can be written:

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

In order to treat ${x}^{2} - 5$ as a difference of squares, we need to recognise that $5 = {\left(\sqrt{5}\right)}^{2}$, then we find:

${x}^{2} - 5 = {x}^{2} - \left({\sqrt{5}}^{2}\right) = \left(x - \sqrt{5}\right) \left(x + \sqrt{5}\right)$

In other words, we let $a = x$ and $b = \sqrt{5}$