Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²-14x+49 

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

Step-1 : Multiply the coefficient of the first term by the constant   1 • 49 = 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 
                     x² - 7x - 7x - 49

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

Multiplying Exponential Expressions :

 1.2    Multiply  (x-7)  by  (x-7) 

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

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

Final result :

  (x - 7)2