Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  x²-22x+121 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -22x  its coefficient is  -22 .
The last term, "the constant", is  +121 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 121 = 121 

Step-2 : Find two factors of  121  whose sum equals the coefficient of the middle term, which is   -22 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -11  and  -11 
                     x² - 11x - 11x - 121

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-11)
              Add up the last 2 terms, pulling out common factors :
                    11 • (x-11)
Step-5 : Add up the four terms of step 4 :
                    (x-11)  •  (x-11)
             Which is the desired factorization

Multiplying Exponential Expressions :

 1.2    Multiply  (x-11)  by  (x-11) 

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

In our case, the common base is  (x-11)  and the exponents are :
          1 , as  (x-11)  is the same number as  (x-11)¹ 
 and   1 , as  (x-11)  is the same number as  (x-11)¹ 
The product is therefore,  (x-11)⁽¹⁺¹⁾ = (x-11)² 

Final result :

  (x - 11)2