Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (34j2 -  18j) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  81j²-18j+1 

The first term is,  81j²  its coefficient is  81 .
The middle term is,  -18j  its coefficient is  -18 .
The last term, "the constant", is  +1 

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

Step-2 : Find two factors of  81  whose sum equals the coefficient of the middle term, which is   -18 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -9 
                     81j² - 9j - 9j - 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    9j • (9j-1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (9j-1)
Step-5 : Add up the four terms of step 4 :
                    (9j-1)  •  (9j-1)
             Which is the desired factorization

Multiplying Exponential Expressions :

 2.2    Multiply  (9j-1)  by  (9j-1) 

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

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

Final result :

  (9j - 1)2