Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (34x2 -  90x) +  25

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  81x²-90x+25 

The first term is,  81x²  its coefficient is  81 .
The middle term is,  -90x  its coefficient is  -90 .
The last term, "the constant", is  +25 

Step-1 : Multiply the coefficient of the first term by the constant   81 • 25 = 2025 

Step-2 : Find two factors of  2025  whose sum equals the coefficient of the middle term, which is   -90 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -45  and  -45 
                     81x² - 45x - 45x - 25

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

Multiplying Exponential Expressions :

 2.2    Multiply  (9x-5)  by  (9x-5) 

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

In our case, the common base is  (9x-5)  and the exponents are :
          1 , as  (9x-5)  is the same number as  (9x-5)¹ 
 and   1 , as  (9x-5)  is the same number as  (9x-5)¹ 
The product is therefore,  (9x-5)⁽¹⁺¹⁾ = (9x-5)² 

Final result :

  (9x - 5)2