# How do you factor 9-72m+144m^2?

May 20, 2017

$9 - 72 m + 144 {m}^{2} = 9 {\left(4 m - 1\right)}^{2}$

#### Explanation:

Note that all of the coefficients are divisible by $9$. Separating that out as a factor first, we can see that the remaining expression is a perfect square trinomial:

$9 - 72 m + 144 {m}^{2} = 9 \left(16 {m}^{2} - 8 m + 1\right)$

$\textcolor{w h i t e}{9 - 72 m + 144 {m}^{2}} = 9 \left({\left(4 m\right)}^{2} - 2 \left(4 m\right) + 1\right)$

$\textcolor{w h i t e}{9 - 72 m + 144 {m}^{2}} = 9 {\left(4 m - 1\right)}^{2}$

$\textcolor{w h i t e}{}$
Footnote

If you know your square numbers, then you might recognise:

$1681 = {41}^{2}$

like:

$16 {m}^{2} - 8 m + 1 = {\left(4 m - 1\right)}^{2}$

This is no coincidence.

When you square $41$, the only carried digit is the one carried into the thousands place.