Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  n²+6n+9 

The first term is,  n²  its coefficient is  1 .
The middle term is,  +6n  its coefficient is  6 .
The last term, "the constant", is  +9 

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

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   6 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  3 
                     n² + 3n + 3n + 9

Step-4 : Add up the first 2 terms, pulling out like factors :
                    n • (n+3)
              Add up the last 2 terms, pulling out common factors :
                    3 • (n+3)
Step-5 : Add up the four terms of step 4 :
                    (n+3)  •  (n+3)
             Which is the desired factorization

Multiplying Exponential Expressions :

 1.2    Multiply  (n+3)  by  (n+3) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (n+3)  and the exponents are :
          1 , as  (n+3)  is the same number as  (n+3)¹ 
 and   1 , as  (n+3)  is the same number as  (n+3)¹ 
The product is therefore,  (n+3)⁽¹⁺¹⁾ = (n+3)² 

Final result :

  (n + 3)2