Solution - Factoring multivariable polynomials

Step  1  :

Equation at the end of step  1  :

  (27 • (a3)) -  26b3
 Step  2  :

Equation at the end of step  2  :

  33a3 -  26b3

Step  3  :

Trying to factor as a Difference of Cubes:

 3.1      Factoring:  27a³-64b³ 

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 :  27  is the cube of  3 

Check :  64  is the cube of   4 
Check :  a³ is the cube of   a¹

Check :  b³ is the cube of   b¹

Factorization is :
             (3a - 4b)  •  (9a² + 12ab + 16b²) 

Trying to factor a multi variable polynomial :

 3.2    Factoring    9a² + 12ab + 16b² 

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

 Factorization fails

Final result :

  (3a - 4b) • (9a2 + 12ab + 16b2)