Solution - Identifying perfect cubes

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "q3"   was replaced by   "q^3".  3 more similar replacement(s).

Step  1  :

Equation at the end of step  1  :

  (((125•(p3))+((75•(p2))•q))+(3•5pq2))+q3
 Step  2  :

Equation at the end of step  2  :

  (((125•(p3))+((3•52p2)•q))+(3•5pq2))+q3
 Step  3  :

Equation at the end of step  3  :

  ((53p3 +  (3•52p2q)) +  (3•5pq2)) +  q3

Step  4  :

Checking for a perfect cube :

 4.1    Factoring:  125p³+75p²q+15pq²+q³ 
 .

  125p³+75p²q+15pq²+q³  is a perfect cube which means it is the cube of another polynomial 

 In our case, the cubic root of  125p³+75p²q+15pq²+q³  is  5p+q  

 Factorization is  (5p+q)³

Final result :

  (5p + q)3