Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•52x2) -  80x) +  16

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   100x² - 80x + 16  =   4 • (25x² - 20x + 4) 

Trying to factor by splitting the middle term

 3.2     Factoring  25x² - 20x + 4 

The first term is,  25x²  its coefficient is  25 .
The middle term is,  -20x  its coefficient is  -20 .
The last term, "the constant", is  +4 

Step-1 : Multiply the coefficient of the first term by the constant   25 • 4 = 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 
                     25x² - 10x - 10x - 4

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

Multiplying Exponential Expressions :

 3.3    Multiply  (5x-2)  by  (5x-2) 

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

In our case, the common base is  (5x-2)  and the exponents are :
          1 , as  (5x-2)  is the same number as  (5x-2)¹ 
 and   1 , as  (5x-2)  is the same number as  (5x-2)¹ 
The product is therefore,  (5x-2)⁽¹⁺¹⁾ = (5x-2)² 

Final result :

  4 • (5x - 2)2