# How do you factor 9m^2-144?

Mar 6, 2017

$9 \left(m - 4\right) \left(m + 4\right)$

#### Explanation:

The first step in factorising is to take out any $\textcolor{b l u e}{\text{common factor}}$

$\Rightarrow 9 {m}^{2} - 144 = 9 \left({m}^{2} - 16\right) \leftarrow \text{ common factor of 9}$

Now ${m}^{2} - 16 \text{ is a " color(blue)"difference of squares}$ and is factorised, in general, as shown.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{For " m^2-16to a=m" and } b = 4$

$\Rightarrow {m}^{2} - 16 = \left(m - 4\right) \left(m + 4\right)$

Putting it all together gives.

$\Rightarrow 9 {m}^{2} - 144 = 9 \left(m - 4\right) \left(m + 4\right)$