Solution - Factoring binomials using the difference of squares

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2". 

Step  1  :

Equation at the end of step  1  :

  (0 -  (6 • (x2))) -  19x20
 Step  2  :

Equation at the end of step  2  :

  (0 -  (2•3x2)) -  19x20

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   -19x²⁰ - 6x²  =   -x² • (19x¹⁸ + 6) 

Trying to factor as a Sum of Cubes :

 4.2      Factoring:  19x¹⁸ + 6 

Theory : A sum 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 :  19  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  -x2 • (19x18 + 6)