SOLUTION: Can you please explain the following in full depth: 3x^2+26xy+16y^2

Question 173291: Can you please explain the following in full depth:
3x^2+26xy+16y^2

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 3 and 16 respectively.

Now multiply the first coefficient 3 and the last coefficient 16 to get 48. Now what two numbers multiply to 48 and add to the middle coefficient 26? Let's list all of the factors of 48:

Factors of 48:
1,2,3,4,6,8,12,16,24,48

-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 48
1*48
2*24
3*16
4*12
6*8
(-1)*(-48)
(-2)*(-24)
(-3)*(-16)
(-4)*(-12)
(-6)*(-8)

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

Now which of these pairs add to 26? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 26

First Number	Second Number	Sum
1	48	1+48=49
2	24	2+24=26
3	16	3+16=19
4	12	4+12=16
6	8	6+8=14
-1	-48	-1+(-48)=-49
-2	-24	-2+(-24)=-26
-3	-16	-3+(-16)=-19
-4	-12	-4+(-12)=-16
-6	-8	-6+(-8)=-14

From this list we can see that 2 and 24 add up to 26 and multiply to 48

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

So this also means that factors to (since is equivalent to )

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Answer:
So factors to

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