factor 27m^2-36m+12

Question

factor this problem

Answer 1

First, what is common between our 3 terms? Interestingly, 3.

 

27m² - 36m + 12 = 3(9m² - 12m + 4)

 

Can we factor our trinomial? I'll show you a way that I learned.

 

9 x 4 = 36

 

What two factors of 36 have a sum of -12? How about -6 and -6?

 

3(9m² - 12m + 36) = 3(9m² - 6m -6m + 4)

 

Now, what do the first two terms have in common? 3m.

 

9m² - 6m = 3m(3m - 2)

 

Now, the last two terms have -2 in common.

 

-6m + 4 = -2(3m - 2)

 

Soooooo...

 

3(9m² -12m + 4) = 3(3m(3m - 2) - 2(3m - 2))

 

Since 3m and -2 are multiplied by 3m - 2, we can add them, except that they are not like terms.

 

3(9m² - 12m + 4) = 3((3m - 2)(3m - 2)) = 3(3m - 2)²

 

 

Answer 2

27m² - 36m + 12 = 3(9m² - 12m + 4) =

3(3m-2)(3m-2) = 3(3m-2)²