Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x3"   was replaced by   "x^3". 

Step  1  :

Equation at the end of step  1  :

  (9 • (x2)) -  (22•32x35)
 Step  2  :

Equation at the end of step  2  :

  32x2 -  (22•32x35)

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   9x² - 36x³⁵  =   -9x² • (4x³³ - 1) 

Trying to factor as a Difference of Cubes:

 4.2      Factoring:  4x³³ - 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 :  4  is not a cube !!

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

Final result :

  -9x2 • (4x33 - 1)