Solution - Factoring binomials using the difference of squares

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "v3"   was replaced by   "v^3".  1 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  ((5x2 • v39) • x) +  54
 Step  2  :

Trying to factor as a Sum of Cubes :

 2.1      Factoring:  5x³v³⁹+54 

Theory : A sum 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 :  5  is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  5x3v39 + 54