Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (26x2 +  16x) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  64x²+16x+1 

The first term is,  64x²  its coefficient is  64 .
The middle term is,  +16x  its coefficient is  16 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   64 • 1 = 64 

Step-2 : Find two factors of  64  whose sum equals the coefficient of the middle term, which is   16 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  8  and  8 
                     64x² + 8x + 8x + 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    8x • (8x+1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (8x+1)
Step-5 : Add up the four terms of step 4 :
                    (8x+1)  •  (8x+1)
             Which is the desired factorization

Multiplying Exponential Expressions :

 2.2    Multiply  (8x+1)  by  (8x+1) 

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

In our case, the common base is  (8x+1)  and the exponents are :
          1 , as  (8x+1)  is the same number as  (8x+1)¹ 
 and   1 , as  (8x+1)  is the same number as  (8x+1)¹ 
The product is therefore,  (8x+1)⁽¹⁺¹⁾ = (8x+1)² 

Final result :

  (8x + 1)2