Question 699636
Ley's break each term down into its factors, then we can see what they have in common.
First term is {{{15x^4y^3}}} this is the same as 
3*5*x*x*x*x*y*y*y
second term is {{{21x^3y^3}}} this is the same as
3*7*x*x*x*y*y*y
and the last term is {{{6x^2y^2}}} 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^2}}}) 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^2}}}) 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^2y^2(5x^2y -7xy +2)}}}
Hope that helps!