Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "f9"   was replaced by   "f^9". 

Step  1  :

Equation at the end of step  1  :

  ((f3)-(5•(f25)))-((4•(f2))-(22•3f9))
 Step  2  :

Equation at the end of step  2  :

  ((f3)-(5•(f25)))-(22f2-(22•3f9))
 Step  3  :

Equation at the end of step  3  :

  ((f3) -  5f25) -  (4f2 - 12f9)

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -5f²⁵ + 12f⁹ + f³ - 4f²  = 

  -f² • (5f²³ - 12f⁷ - f + 4) 

Checking for a perfect cube :

 5.2    5f²³ - 12f⁷ - f + 4  is not a perfect cube

Trying to factor by pulling out :

 5.3      Factoring:  5f²³ - 12f⁷ - f + 4 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -f + 4 
Group 2:  -12f⁷ + 5f²³ 

Pull out from each group separately :

Group 1:   (-f + 4) • (1) = (f - 4) • (-1)
Group 2:   (5f¹⁶ - 12) • (f⁷)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Final result :

  -f2 • (5f23 - 12f7 - f + 4)