Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  r²-6r+9 

The first term is,  r²  its coefficient is  1 .
The middle term is,  -6r  its coefficient is  -6 .
The last term, "the constant", is  +9 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 9 = 9 

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   -6 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  -3 
                     r² - 3r - 3r - 9

Step-4 : Add up the first 2 terms, pulling out like factors :
                    r • (r-3)
              Add up the last 2 terms, pulling out common factors :
                    3 • (r-3)
Step-5 : Add up the four terms of step 4 :
                    (r-3)  •  (r-3)
             Which is the desired factorization

Multiplying Exponential Expressions :

 1.2    Multiply  (r-3)  by  (r-3) 

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

In our case, the common base is  (r-3)  and the exponents are :
          1 , as  (r-3)  is the same number as  (r-3)¹ 
 and   1 , as  (r-3)  is the same number as  (r-3)¹ 
The product is therefore,  (r-3)⁽¹⁺¹⁾ = (r-3)² 

Final result :

  (r - 3)2