Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3n2 -  24n) +  48

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   3n² - 24n + 48  =   3 • (n² - 8n + 16) 

Trying to factor by splitting the middle term

 3.2     Factoring  n² - 8n + 16 

The first term is,  n²  its coefficient is  1 .
The middle term is,  -8n  its coefficient is  -8 .
The last term, "the constant", is  +16 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 16 = 16 

Step-2 : Find two factors of  16  whose sum equals the coefficient of the middle term, which is   -8 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -4  and  -4 
                     n² - 4n - 4n - 16

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

Multiplying Exponential Expressions :

 3.3    Multiply  (n-4)  by  (n-4) 

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

In our case, the common base is  (n-4)  and the exponents are :
          1 , as  (n-4)  is the same number as  (n-4)¹ 
 and   1 , as  (n-4)  is the same number as  (n-4)¹ 
The product is therefore,  (n-4)⁽¹⁺¹⁾ = (n-4)² 

Final result :

  3 • (n - 4)2