Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (26t2 -  112t) +  49

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  64t²-112t+49 

The first term is,  64t²  its coefficient is  64 .
The middle term is,  -112t  its coefficient is  -112 .
The last term, "the constant", is  +49 

Step-1 : Multiply the coefficient of the first term by the constant   64 • 49 = 3136 

Step-2 : Find two factors of  3136  whose sum equals the coefficient of the middle term, which is   -112 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -56  and  -56 
                     64t² - 56t - 56t - 49

Step-4 : Add up the first 2 terms, pulling out like factors :
                    8t • (8t-7)
              Add up the last 2 terms, pulling out common factors :
                    7 • (8t-7)
Step-5 : Add up the four terms of step 4 :
                    (8t-7)  •  (8t-7)
             Which is the desired factorization

Multiplying Exponential Expressions :

 2.2    Multiply  (8t-7)  by  (8t-7) 

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

In our case, the common base is  (8t-7)  and the exponents are :
          1 , as  (8t-7)  is the same number as  (8t-7)¹ 
 and   1 , as  (8t-7)  is the same number as  (8t-7)¹ 
The product is therefore,  (8t-7)⁽¹⁺¹⁾ = (8t-7)² 

Final result :

  (8t - 7)2