Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  u²-14u+49 

The first term is,  u²  its coefficient is  1 .
The middle term is,  -14u  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 
                     u² - 7u - 7u - 49

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

Multiplying Exponential Expressions :

 1.2    Multiply  (u-7)  by  (u-7) 

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

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

Final result :

  (u - 7)2