Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (72x2 +  14x) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  49x²+14x+1 

The first term is,  49x²  its coefficient is  49 .
The middle term is,  +14x  its coefficient is  14 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   49 • 1 = 49 

Step-2 : Find two factors of  49  whose sum equals the coefficient of the middle term, which is   14 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  7  and  7 
                     49x² + 7x + 7x + 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    7x • (7x+1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (7x+1)
Step-5 : Add up the four terms of step 4 :
                    (7x+1)  •  (7x+1)
             Which is the desired factorization

Multiplying Exponential Expressions :

 2.2    Multiply  (7x+1)  by  (7x+1) 

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

In our case, the common base is  (7x+1)  and the exponents are :
          1 , as  (7x+1)  is the same number as  (7x+1)¹ 
 and   1 , as  (7x+1)  is the same number as  (7x+1)¹ 
The product is therefore,  (7x+1)⁽¹⁺¹⁾ = (7x+1)² 

Final result :

  (7x + 1)2