Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (((x4)-(16•(y4)))-((4•(x3))•y))+24xy3
 Step  2  :

Equation at the end of step  2  :

  (((x4)-(16•(y4)))-(22x3•y))+24xy3
 Step  3  :

Equation at the end of step  3  :

  (((x4) -  24y4) -  22x3y) +  24xy3

Step  4  :

Checking for a perfect cube :

 4.1    x⁴-4x³y+16xy³-16y⁴  is not a perfect cube

Final result :

  x4 - 4x3y + 16xy3 - 16y4