SOLUTION: what is the greatest common factor of 15x^4y^3-21x^3y^3+6x^2y^2

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Question 699636: what is the greatest common factor of 15x^4y^3-21x^3y^3+6x^2y^2
Answer by Simnepi(216) About Me  (Show Source):
You can put this solution on YOUR website!
Ley's break each term down into its factors, then we can see what they have in common.
First term is 15x%5E4y%5E3 this is the same as
3*5*x*x*x*x*y*y*y
second term is 21x%5E3y%5E3 this is the same as
3*7*x*x*x*y*y*y
and the last term is 6x%5E2y%5E2 which is the same as
3*2*x*x*y*y
Now if we look at each of the broken down terms we can see they all have a 3 in common so that can be taken out as a common factor
look again and we see that they all have x*x (x%5E2) in them too (we can't take any more x's out as there are only 2 of them in the last term!)
Look one more time and we see that they also all have y*y (y%5E2) in them which can be removed as a common factor.
All those factors should be placed outside of a bracket and what is left of the term placed inside the bracket, i.e.
3*x*x*y*y(5*x*x*y -7*x*y +2)
Putting the terms back together again gives
3x%5E2y%5E2%285x%5E2y+-7xy+%2B2%29
Hope that helps!