SOLUTION: Factor completely: m^3-9m^2n+18n^2m If anyone could help I would appricate it, I came up with m(m^2-9mn+18n^2) but it doesnt look right for some reason.

Question 120534: Factor completely: m^3-9m^2n+18n^2m
If anyone could help I would appricate it, I came up with m(m^2-9mn+18n^2) but it doesnt look right for some reason.
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

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Looking at we can see that the first term is and the last term is where the coefficients are 1 and 18 respectively.

Now multiply the first coefficient 1 and the last coefficient 18 to get 18. Now what two numbers multiply to 18 and add to the middle coefficient -9? Let's list all of the factors of 18:

Factors of 18:
1,2,3,6,9,18

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

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

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

Now which of these pairs add to -9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -9

First Number Second Number Sum
1 18 1+18=19
2 9 2+9=11
3 6 3+6=9
-1 -18 -1+(-18)=-19
-2 -9 -2+(-9)=-11
-3 -6 -3+(-6)=-9

From this list we can see that -3 and -6 add up to -9 and multiply to 18

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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So our expression goes from and factors further to

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Answer:

So factors to

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

Just carry this one step further
answer

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First Number	Second Number	Sum
1	18	1+18=19
2	9	2+9=11
3	6	3+6=9
-1	-18	-1+(-18)=-19
-2	-9	-2+(-9)=-11
-3	-6	-3+(-6)=-9