Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  z²-12z+36 

The first term is,  z²  its coefficient is  1 .
The middle term is,  -12z  its coefficient is  -12 .
The last term, "the constant", is  +36 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 36 = 36 

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -12 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  -6 
                     z² - 6z - 6z - 36

Step-4 : Add up the first 2 terms, pulling out like factors :
                    z • (z-6)
              Add up the last 2 terms, pulling out common factors :
                    6 • (z-6)
Step-5 : Add up the four terms of step 4 :
                    (z-6)  •  (z-6)
             Which is the desired factorization

Multiplying Exponential Expressions :

 1.2    Multiply  (z-6)  by  (z-6) 

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

In our case, the common base is  (z-6)  and the exponents are :
          1 , as  (z-6)  is the same number as  (z-6)¹ 
 and   1 , as  (z-6)  is the same number as  (z-6)¹ 
The product is therefore,  (z-6)⁽¹⁺¹⁾ = (z-6)² 

Final result :

  (z - 6)2