Solution - Identifying perfect cubes

Step  1  :

Equation at the end of step  1  :

  (((0-((5•(x5))•(y3)))-(5•(x2)))-((15•(x4))•(y2)))-((3•5x3)•y)
 Step  2  :

Equation at the end of step  2  :

  (((0-((5•(x5))•(y3)))-(5•(x2)))-((3•5x4)•y2))-(3•5x3y)
 Step  3  :

Equation at the end of step  3  :

  (((0-((5•(x5))•(y3)))-5x2)-(3•5x4y2))-(3•5x3y)
 Step  4  :

Equation at the end of step  4  :

  (((0 -  (5x5 • y3)) -  5x2) -  (3•5x4y2)) -  (3•5x3y)

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -5x⁵y³ - 15x⁴y² - 15x³y - 5x²  = 

  -5x² • (x³y³ + 3x²y² + 3xy + 1) 

Checking for a perfect cube :

 6.2    Factoring:  x³y³ + 3x²y² + 3xy + 1 
 .

  x³y³ + 3x²y² + 3xy + 1  is a perfect cube which means it is the cube of another polynomial 

 In our case, the cubic root of  x³y³ + 3x²y² + 3xy + 1  is  xy + 1  

 Factorization is  (xy + 1)³

Final result :

  -5x2 • (xy + 1)3