Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((24•32s2) -  264s) +  121

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  144s²-264s+121 

The first term is,  144s²  its coefficient is  144 .
The middle term is,  -264s  its coefficient is  -264 .
The last term, "the constant", is  +121 

Step-1 : Multiply the coefficient of the first term by the constant   144 • 121 = 17424 

Step-2 : Find two factors of  17424  whose sum equals the coefficient of the middle term, which is   -264 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -132  and  -132 
                     144s² - 132s - 132s - 121

Step-4 : Add up the first 2 terms, pulling out like factors :
                    12s • (12s-11)
              Add up the last 2 terms, pulling out common factors :
                    11 • (12s-11)
Step-5 : Add up the four terms of step 4 :
                    (12s-11)  •  (12s-11)
             Which is the desired factorization

Multiplying Exponential Expressions :

 2.2    Multiply  (12s-11)  by  (12s-11) 

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

In our case, the common base is  (12s-11)  and the exponents are :
          1 , as  (12s-11)  is the same number as  (12s-11)¹ 
 and   1 , as  (12s-11)  is the same number as  (12s-11)¹ 
The product is therefore,  (12s-11)⁽¹⁺¹⁾ = (12s-11)² 

Final result :

  (12s - 11)2