Solution - Factoring multivariable polynomials

Step  1  :

Trying to factor as a Difference of Cubes:

 1.1      Factoring:  m⁹-n¹⁵ 

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 :  m⁹ is the cube of   m³

Check :  n¹⁵ is the cube of   n⁵

Factorization is :
             (m³ - n⁵)  •  (m⁶ + m³n⁵ + n¹⁰) 

Trying to factor a multi variable polynomial :

 1.2    Factoring    m⁶ + m³n⁵ + n¹⁰ 

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

 Factorization fails

Final result :

  (m3 - n5) • (m6 + m3n5 + n10)