Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (32f2 -  f) -  8

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  9f²-f-8 

The first term is,  9f²  its coefficient is  9 .
The middle term is,  -f  its coefficient is  -1 .
The last term, "the constant", is  -8 

Step-1 : Multiply the coefficient of the first term by the constant   9 • -8 = -72 

Step-2 : Find two factors of  -72  whose sum equals the coefficient of the middle term, which is   -1 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  8 
                     9f² - 9f + 8f - 8

Step-4 : Add up the first 2 terms, pulling out like factors :
                    9f • (f-1)
              Add up the last 2 terms, pulling out common factors :
                    8 • (f-1)
Step-5 : Add up the four terms of step 4 :
                    (9f+8)  •  (f-1)
             Which is the desired factorization

Final result :

  (f - 1) • (9f + 8)