Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (((5•(n33))•(n2))-2n)-((3n-(7•(n3)))-22n2)
 Step  2  :

Equation at the end of step  2  :

  (((5•(n33))•(n2))-2n)-((3n-7n3)-22n2)
 Step  3  :

Equation at the end of step  3  :

  ((5n33 • n2) -  2n) -  (-7n3 - 4n2 + 3n)

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   5n³⁵ + 7n³ + 4n² - 5n  = 

  n • (5n³⁴ + 7n² + 4n - 5) 

Checking for a perfect cube :

 5.2    5n³⁴ + 7n² + 4n - 5  is not a perfect cube

Trying to factor by pulling out :

 5.3      Factoring:  5n³⁴ + 7n² + 4n - 5 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  4n - 5 
Group 2:  5n³⁴ + 7n² 

Pull out from each group separately :

Group 1:   (4n - 5) • (1)
Group 2:   (5n³² + 7) • (n²)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Final result :

  n • (5n34 + 7n2 + 4n - 5)