Question 353698
{{{(2x-7)^3(6)(4x+1)^5(4)+(4x+1)^6(3)(2x-7)^2(2)}}}
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:
{{{(2x-7)^2*(2x-7)(6)(4x+1)^5(4)+(4x+1)^5*(4x+1)(6)(2x-7)^2}}}
Now I wil make the GCF in each half red:
{{{red((2x-7)^2)*(2x-7)red((6))red((4x+1)^5)(4)+red((4x+1)^5)*(4x+1)red((6))red((2x-7)^2)}}}
Factoring out the GCF (in red) from each half we get:
{{{(2x-7)^2*(6)*(4x+1)^5*((2x-7)(4) + (4x+1))}}}
The simplifying part comes from simplifying the second factor:
{{{(2x-7)^2*(6)*(4x+1)^5*(8x-28+4x+1)}}}
{{{(2x-7)^2*(6)*(4x+1)^5*(12x-27)}}}
When factoring we keep factoring until we cannot factor any further. The second factor above has a GCF of 3 which we can factor:
{{{(2x-7)^2*(6)*(4x+1)^5*3(4x-9)}}}
And last of all the the constant factors can be combined to make 18 (which is usually put in front:
{{{18*(2x-7)^2*(4x+1)^5(4x-9)}}}