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

1 Answer
May 20, 2017

Answer:

#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.