Solution - Simplification or other simple results

Step  1  :

Trying to factor by splitting the middle term

 1.1     Factoring  y²-20y+100 

The first term is,  y²  its coefficient is  1 .
The middle term is,  -20y  its coefficient is  -20 .
The last term, "the constant", is  +100 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 100 = 100 

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   -20 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  -10 
                     y² - 10y - 10y - 100

Step-4 : Add up the first 2 terms, pulling out like factors :
                    y • (y-10)
              Add up the last 2 terms, pulling out common factors :
                    10 • (y-10)
Step-5 : Add up the four terms of step 4 :
                    (y-10)  •  (y-10)
             Which is the desired factorization

Multiplying Exponential Expressions :

 1.2    Multiply  (y-10)  by  (y-10) 

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

In our case, the common base is  (y-10)  and the exponents are :
          1 , as  (y-10)  is the same number as  (y-10)¹ 
 and   1 , as  (y-10)  is the same number as  (y-10)¹ 
The product is therefore,  (y-10)⁽¹⁺¹⁾ = (y-10)² 

Final result :

  (y - 10)2