Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((2•5n2) +  100n) +  250

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   10n² + 100n + 250  =   10 • (n² + 10n + 25) 

Trying to factor by splitting the middle term

 3.2     Factoring  n² + 10n + 25 

The first term is,  n²  its coefficient is  1 .
The middle term is,  +10n  its coefficient is  10 .
The last term, "the constant", is  +25 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 25 = 25 

Step-2 : Find two factors of  25  whose sum equals the coefficient of the middle term, which is   10 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  5  and  5 
                     n² + 5n + 5n + 25

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

Multiplying Exponential Expressions :

 3.3    Multiply  (n+5)  by  (n+5) 

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

In our case, the common base is  (n+5)  and the exponents are :
          1 , as  (n+5)  is the same number as  (n+5)¹ 
 and   1 , as  (n+5)  is the same number as  (n+5)¹ 
The product is therefore,  (n+5)⁽¹⁺¹⁾ = (n+5)² 

Final result :

  10 • (n + 5)2