Solution - Factoring multivariable polynomials

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "s3"   was replaced by   "s^3".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (t3) -  53s3
 Step  2  :

Trying to factor as a Difference of Cubes:

 2.1      Factoring:  t³-125s³ 

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 :  125  is the cube of   5 
Check :  t³ is the cube of   t¹

Check :  s³ is the cube of   s¹

Factorization is :
             (t - 5s)  •  (t² + 5ts + 25s²) 

Trying to factor a multi variable polynomial :

 2.2    Factoring    t² + 5ts + 25s² 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Final result :

  (t - 5s) • (t2 + 5ts + 25s2)