SOLUTION: Factor 15m^3n +20mn^2 -10m^2n

Question 1003557: Factor 15m^3n +20mn^2 -10m^2n
Found 2 solutions by addingup, smithsac:
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
Factor 5mn out of 15m^3n+20mn^2-10m^2n:
Answer:5mn(3m^2+4n-2m)
Answer by smithsac(2) (Show Source): You can put this solution on YOUR website!
To Factor simply start with GCF(greatest common factor)for each number and letter:
so taking the whole numbers first: 15, 20, 10
There GCF is the number 5 (like 5x3 = 15 5x4=20 5x2=10) all have the factor 5
ok, so we will USE THE NUMBER 5 for the first digit to our answer
Next, look at the first letter which is m {the first m is m^3, the second m is simply just m, the third m is m^2}
Based on the number of exponents the GCF for m is m (like m*m*m = m^3, m*1=m then m*m = m^ they all have at least one m in common)
So our SECOND digit after 5 is now m
Do the same thing with the letter n:
First one is n, second is n^2 and the third is n (n*1, n*n, n*1 - they all have at least one n in common)
SO OUR Third digit after 5m is n
So now using 5mn we figure out the rest which is put into parenthesis:
working backwards from your original equation above we see 15m^3n is now split up as 5mn(3m^2) [This means if we were to multiply - the answer would result with 15m^3n]
So now we do the same with 20mn^2 is now split up as 5mn(4n)
Then finally 10m^2n is now split up as 5mn(2m)
Putting these all together we get the answer as
5mn(3m^2 + 4n - 2m)

To see if you're correct, simply do the distributive property and you'll see you'll end up with original equation which means you factored it correctly.
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