Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (34x2 -  36x) +  4

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  81x²-36x+4 

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

Step-1 : Multiply the coefficient of the first term by the constant   81 • 4 = 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 
                     81x² - 18x - 18x - 4

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

Multiplying Exponential Expressions :

 2.2    Multiply  (9x-2)  by  (9x-2) 

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

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

Final result :

  (9x - 2)2