Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  26y3 -  1

Step  2  :

Trying to factor as a Difference of Cubes:

 2.1      Factoring:  64y³-1 

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into
              (a-b) • (a² +ab +b²)

Proof :  (a-b)•(a²+ab+b²) =
            a³+a²b+ab²-ba²-b²a-b³ =
            a³+(a²b-ba²)+(ab²-b²a)-b³ =
            a³+0+0-b³ =
            a³-b³

Check :  64  is the cube of  4 

Check :  1  is the cube of   1 
Check :  y³ is the cube of   y¹

Factorization is :
             (4y - 1)  •  (16y² + 4y + 1) 

Trying to factor by splitting the middle term

 2.2     Factoring  16y² + 4y + 1 

The first term is,  16y²  its coefficient is  16 .
The middle term is,  +4y  its coefficient is  4 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   16 • 1 = 16 

Step-2 : Find two factors of  16  whose sum equals the coefficient of the middle term, which is   4 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  (4y - 1) • (16y2 + 4y + 1)