Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "y2"   was replaced by   "y^2". 

Step  1  :

Equation at the end of step  1  :

  (23y2 +  6y) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  8y²+6y+1 

The first term is,  8y²  its coefficient is  8 .
The middle term is,  +6y  its coefficient is  6 .
The last term, "the constant", is  +1 

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

Step-2 : Find two factors of  8  whose sum equals the coefficient of the middle term, which is   6 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  4 
                     8y² + 2y + 4y + 1

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

Final result :

  (4y + 1) • (2y + 1)