Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (22x2 -  36x) +  81

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  4x²-36x+81 

The first term is,  4x²  its coefficient is  4 .
The middle term is,  -36x  its coefficient is  -36 .
The last term, "the constant", is  +81 

Step-1 : Multiply the coefficient of the first term by the constant   4 • 81 = 324 

Step-2 : Find two factors of  324  whose sum equals the coefficient of the middle term, which is   -36 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -18  and  -18 
                     4x² - 18x - 18x - 81

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (2x-9)
              Add up the last 2 terms, pulling out common factors :
                    9 • (2x-9)
Step-5 : Add up the four terms of step 4 :
                    (2x-9)  •  (2x-9)
             Which is the desired factorization

Multiplying Exponential Expressions :

 2.2    Multiply  (2x-9)  by  (2x-9) 

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

In our case, the common base is  (2x-9)  and the exponents are :
          1 , as  (2x-9)  is the same number as  (2x-9)¹ 
 and   1 , as  (2x-9)  is the same number as  (2x-9)¹ 
The product is therefore,  (2x-9)⁽¹⁺¹⁾ = (2x-9)² 

Final result :

  (2x - 9)2