Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (52t2 -  100t) +  100

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   25t² - 100t + 100  =   25 • (t² - 4t + 4) 

Trying to factor by splitting the middle term

 3.2     Factoring  t² - 4t + 4 

The first term is,  t²  its coefficient is  1 .
The middle term is,  -4t  its coefficient is  -4 .
The last term, "the constant", is  +4 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 4 = 4 

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   -4 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  -2 
                     t² - 2t - 2t - 4

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

Multiplying Exponential Expressions :

 3.3    Multiply  (t-2)  by  (t-2) 

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

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

Final result :

  25 • (t - 2)2