Question 1003557
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.