SOLUTION: Factor Completely. 9x^2+12xy+4y^2-25. Thanks

Question 117381: Factor Completely.
9x^2+12xy+4y^2-25.
Thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First let's factor

Looking at we can see that the first term is and the last term is where the coefficients are 9 and 4 respectively.

Now multiply the first coefficient 9 and the last coefficient 4 to get 36. Now what two numbers multiply to 36 and add to the middle coefficient 12? Let's list all of the factors of 36:

Factors of 36:
1,2,3,4,6,9,12,18

-1,-2,-3,-4,-6,-9,-12,-18 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 36
1*36
2*18
3*12
4*9
6*6
(-1)*(-36)
(-2)*(-18)
(-3)*(-12)
(-4)*(-9)
(-6)*(-6)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 12? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 12

First Number	Second Number	Sum
1	36	1+36=37
2	18	2+18=20
3	12	3+12=15
4	9	4+9=13
6	6	6+6=12
-1	-36	-1+(-36)=-37
-2	-18	-2+(-18)=-20
-3	-12	-3+(-12)=-15
-4	-9	-4+(-9)=-13
-6	-6	-6+(-6)=-12

From this list we can see that 6 and 6 add up to 12 and multiply to 36

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to which also looks like

So we now have

Now factor the expression using the difference of squares

------------------------------------------
Answer:

So factors to
RELATED QUESTIONS
Factor completely 9x^2 + 12xy + 4y^2 +... (answered by fractalier,stanbon)

factor completely... (answered by psbhowmick)

Factor the following completely: 9x^2 + 12xy + 4y^2 - 25 (answered by funmath)

Factor completely. 9x^2 + 12xy + 4y^2 -25 (answered by checkley75)

Factor Completely 9x^2 + 12xy + 4y^2 -... (answered by stanbon)

factor completely... (answered by ramkikk66)

I am having problems with this problem. Factor completely. 9x^2 + 12xy + 4y^2... (answered by checkley71)

how can i factor this completely?... (answered by checkley75,Earlsdon)

Factor completely. I dont understand... (answered by stanbon)