Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (32a2 -  10a) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  9a²-10a+1 

The first term is,  9a²  its coefficient is  9 .
The middle term is,  -10a  its coefficient is  -10 .
The last term, "the constant", is  +1 

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

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   -10 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -1 
                     9a² - 9a - 1a - 1

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

Final result :

  (a - 1) • (9a - 1)