Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•5y2) -  7y) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  10y²-7y+1 

The first term is,  10y²  its coefficient is  10 .
The middle term is,  -7y  its coefficient is  -7 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   10 • 1 = 10 

Step-2 : Find two factors of  10  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  -2 
                     10y² - 5y - 2y - 1

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

Final result :

  (2y - 1) • (5y - 1)