SOLUTION: Hello! Could someone help me with these questions? Fully factor each of the following: a) 16m^2-n^2-16m+4 b) -3xy+6+2y-9x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello! Could someone help me with these questions? Fully factor each of the following: a) 16m^2-n^2-16m+4 b) -3xy+6+2y-9x      Log On


   

Question 937089: Hello! Could someone help me with these questions?
Fully factor each of the following:
a) 16m^2-n^2-16m+4
b) -3xy+6+2y-9x
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
16m%5E2-n%5E2-16m%2B4

Group the first third and fourth terms as a square trinomial:

%2816m%5E2-16m%2B4%29-n%5E2

Factor the trinomial 16m%5E2-16m%2B4=4%284m%5E2-4m%2B1%29=4%282m-1%29%282m-1%29=4%282m-1%29%5E2

4%282m-1%29%5E2-n%5E2

That's the difference of two squares:

[2(2m-1)-n][2(2m-1)+n]

[4m-2-n][4m-2+n]

----------------
-3xy+6+2y-9x

Notice that 6 is 3 times 2 and -9 is 3 times -3.
So rearrange the terms like this, positive ones first and
negative ones last:

6+2y-9x-3xy

Factor the first two by taking out a 2.
Factor the last two by taking out -3x

2(3+y)-3x(3+y)

Take out common factor (3+y)

(3+y)(2-3x)

Edwin