Solution - Factoring binomials using the difference of squares

Step  1  :

Step  2  :

Pulling out like terms :

 2.1     Pull out like factors :

   -x²⁴ - 2  =   -1 • (x²⁴ + 2) 

Trying to factor as a Sum of Cubes :

 2.2      Factoring:  x²⁴ + 2 

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 :  2  is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

  -x24 - 2