Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "y7"   was replaced by   "y^7". 

Step  1  :

Equation at the end of step  1  :

  (x2) -  (23xy7 • y2)
 Step  2  :
 Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   x² - 8xy⁹  =   x • (x - 8y⁹) 

Trying to factor as a Difference of Cubes:

 3.2      Factoring:  x - 8y⁹ 

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 :  8  is the cube of   2 
Check :  x ¹ is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  x • (x - 8y9)