Question

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

Answer 1

`9-72m+144m^2 = 9(4m-1)^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:

`9-72m+144m^2 = 9(16m^2-8m+1)`

`color(white)(9-72m+144m^2) = 9((4m)^2-2(4m)+1)`

`color(white)(9-72m+144m^2) = 9(4m-1)^2`

`color(white)()`
Footnote

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

`1681 = 41^2`

like:

`16m^2-8m+1 = (4m-1)^2`

This is no coincidence.

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