# How do you write q^2 – 12q + 36 in factored form?

Sep 21, 2015

${q}^{2} - 12 q + 36 = {\left(q - 6\right)}^{2}$

#### Explanation:

So, to factorise this quadratic expression we need to find numbers that add together to make -12 and multiply together to make +36. The only two numbers that do this are -6 and -6.

Or,

${q}^{2} - 12 q + 36 = \left(q - 6\right) \left(q - 6\right) = {\left(q - 6\right)}^{2}$

Sep 21, 2015

${\left(q - 6\right)}^{2}$

#### Explanation:

It is a perfect square -
${q}^{2} - 6 q - 6 q + 36$
$q \left(q - 6\right) - 6 \left(q - 6\right)$
$\left(q - 6\right) \left(q - 6\right)$
${\left(q - 6\right)}^{2}$

Sep 21, 2015

${\left(q - 6\right)}^{2}$

#### Explanation:

Actually, if you look at it closely, you'll realize that ${q}^{2} - 12 q + 36$ is a perfect square trinomial. You can write it down as $\left(q - 6\right) \left(q - 6\right)$ or simply ${\left(q - 6\right)}^{2}$.