Question 146465: I need help with some math problems Please
factor the following polynomials
24x^3y -8xy^2
16x^2-24xy+9y^2
5r^3-5
(36x^2-49y^2) Thanks alot for your help!!!!!
Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983)   (Show Source):
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! I'll do the first two to get you started
# 1
 Start with the given expression
 Factor out the GCF 
# 2
Looking at  we can see that the first term is  and the last term is  where the coefficients are 16 and 9 respectively.
Now multiply the first coefficient 16 and the last coefficient 9 to get 144. Now what two numbers multiply to 144 and add to the middle coefficient -24? Let's list all of the factors of 144:
Factors of 144:
1,2,3,4,6,8,9,12,16,18,24,36,48,72
-1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 144
1*144
2*72
3*48
4*36
6*24
8*18
9*16
12*12
(-1)*(-144)
(-2)*(-72)
(-3)*(-48)
(-4)*(-36)
(-6)*(-24)
(-8)*(-18)
(-9)*(-16)
(-12)*(-12)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -24? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -24
| First Number | Second Number | Sum | | 1 | 144 | 1+144=145 | | 2 | 72 | 2+72=74 | | 3 | 48 | 3+48=51 | | 4 | 36 | 4+36=40 | | 6 | 24 | 6+24=30 | | 8 | 18 | 8+18=26 | | 9 | 16 | 9+16=25 | | 12 | 12 | 12+12=24 | | -1 | -144 | -1+(-144)=-145 | | -2 | -72 | -2+(-72)=-74 | | -3 | -48 | -3+(-48)=-51 | | -4 | -36 | -4+(-36)=-40 | | -6 | -24 | -6+(-24)=-30 | | -8 | -18 | -8+(-18)=-26 | | -9 | -16 | -9+(-16)=-25 | | -12 | -12 | -12+(-12)=-24 |
From this list we can see that -12 and -12 add up to -24 and multiply to 144
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 )
note: is equivalent to  since the term occurs twice. So also factors to
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Answer:
So factors to
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