6.

 

24a^3b^2+48ab^3-42a^4b

Factor out the greatest common factor. The biggest number that

goes into all of the coefficients is 6. All of the terms have at least one

factor of a and one factor of b. Factor out a 6ab

 

6ab(4a^2b+8b^2-7a^3)

 

We can tell that we have factored out the greatest common

factor because there is no common factor for the terms in the

parentheses.

 

At this point we see if there is some other way that the

expression inside the parentheses can be factored in any other way,

but it cannot.