SOLUTION: I know how to simplify and I know how to factor but I am not sure what is being asked of me when I asked to do both. Here is an example; Factor and simplify. {{{(2x-7)^3(6)(4x+1)

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: I know how to simplify and I know how to factor but I am not sure what is being asked of me when I asked to do both. Here is an example; Factor and simplify. {{{(2x-7)^3(6)(4x+1)      Log On


   

Question 353698: I know how to simplify and I know how to factor but I am not sure what is being asked of me when I asked to do both. Here is an example;
Factor and simplify.
%282x-7%29%5E3%286%29%284x%2B1%29%5E5%284%29%2B%284x%2B1%29%5E6%283%29%282x-7%29%5E2%282%29
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-7%29%5E3%286%29%284x%2B1%29%5E5%284%29%2B%284x%2B1%29%5E6%283%29%282x-7%29%5E2%282%29
The "+" sign after the "(4)" in the above expression separates it into two halves. We are going to factor by trying to find the Greatest Common Factor (GCF) of the two halves. In order to make the GCF clearer, I am going to rewrite each half in an way where the GCF will become more obvious:

Now I wil make the GCF in each half red:

Factoring out the GCF (in red) from each half we get:
%282x-7%29%5E2%2A%286%29%2A%284x%2B1%29%5E5%2A%28%282x-7%29%284%29+%2B+%284x%2B1%29%29
The simplifying part comes from simplifying the second factor:
%282x-7%29%5E2%2A%286%29%2A%284x%2B1%29%5E5%2A%288x-28%2B4x%2B1%29
%282x-7%29%5E2%2A%286%29%2A%284x%2B1%29%5E5%2A%2812x-27%29
When factoring we keep factoring until we cannot factor any further. The second factor above has a GCF of 3 which we can factor:
%282x-7%29%5E2%2A%286%29%2A%284x%2B1%29%5E5%2A3%284x-9%29
And last of all the the constant factors can be combined to make 18 (which is usually put in front:
18%2A%282x-7%29%5E2%2A%284x%2B1%29%5E5%284x-9%29