Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (2•33x4) -  16x

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   54x⁴ - 16x  =   2x • (27x³ - 8) 

Trying to factor as a Difference of Cubes:

 3.2      Factoring:  27x³ - 8 

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 :  8  is the cube of   2 
Check :  x³ is the cube of   x¹

Factorization is :
             (3x - 2)  •  (9x² + 6x + 4) 

Trying to factor by splitting the middle term

 3.3     Factoring  9x² + 6x + 4 

The first term is,  9x²  its coefficient is  9 .
The middle term is,  +6x  its coefficient is  6 .
The last term, "the constant", is  +4 

Step-1 : Multiply the coefficient of the first term by the constant   9 • 4 = 36 

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   6 .

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  2x • (3x - 2) • (9x2 + 6x + 4)