# How do you factor x^2 +8x -24?

Aug 28, 2016

${x}^{2} + 8 x - 24 = \left(x + 4 - 2 \sqrt{10}\right) \left(x + 4 + 2 \sqrt{10}\right)$

#### Explanation:

The difference of squares identity can be written:

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

Use this with $a = \left(x + 4\right)$ and $b = 2 \sqrt{10}$ as follows:

${x}^{2} + 8 x - 24$

$= {x}^{2} + 8 x + 16 - 40$

$= {\left(x + 4\right)}^{2} - {\left(2 \sqrt{10}\right)}^{2}$

$= \left(\left(x + 4\right) - 2 \sqrt{10}\right) \left(\left(x + 4\right) + 2 \sqrt{10}\right)$

$= \left(x + 4 - 2 \sqrt{10}\right) \left(x + 4 + 2 \sqrt{10}\right)$