# How do you factor 7c²-28c+7 ?

Aug 24, 2016

$7 {c}^{2} - 28 c + 7 = 7 \left(c - 2 - \sqrt{3}\right) \left(c - 2 + \sqrt{3}\right)$

#### 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 $a = \left(c - 2\right)$ and $b = \sqrt{3}$ as follows:

$7 {c}^{2} - 28 c + 7$

$= 7 \left({c}^{2} - 4 c + 1\right)$

$= 7 \left({c}^{2} - 4 c + 4 - 3\right)$

$= 7 \left({\left(c - 2\right)}^{2} - {\left(\sqrt{3}\right)}^{2}\right)$

$= 7 \left(\left(c - 2\right) - \sqrt{3}\right) \left(\left(c - 2\right) + \sqrt{3}\right)$

$= 7 \left(c - 2 - \sqrt{3}\right) \left(c - 2 + \sqrt{3}\right)$