Solution - Factoring multivariable polynomials

Step  1  :

Trying to factor as a Difference of Cubes:

 1.1      Factoring:  a³-b³ 

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 :  a³ is the cube of   a¹

Check :  b³ is the cube of   b¹

Factorization is :
             (a - b)  •  (a² + ab + b²) 

Trying to factor a multi variable polynomial :

 1.2    Factoring    a² + ab + b² 

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

 Factorization fails

Final result :

  (a - b) • (a2 + ab + b2)