4x2-28x+49  
Final result :
  (2x - 7)2
Step by step solution :
Step  1  :
Equation at the end of step  1  :
  (22x2 -  28x) +  49
Step  2  :
Trying to factor by splitting the middle term
 2.1     Factoring  4x2-28x+49  
The first term is,  4x2  its coefficient is  4 .
The middle term is,  -28x  its coefficient is  -28 .
The last term, "the constant", is  +49  
Step-1 : Multiply the coefficient of the first term by the constant   4 • 49 = 196  
Step-2 : Find two factors of  196  whose sum equals the coefficient of the middle term, which is   -28 .
      -196    +    -1    =    -197  
      -98    +    -2    =    -100  
      -49    +    -4    =    -53  
      -28    +    -7    =    -35  
      -14    +    -14    =    -28    That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -14  and  -14  
                     4x2 - 14x - 14x - 49
Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (2x-7)
              Add up the last 2 terms, pulling out common factors :
                    7 • (2x-7)
Step-5 : Add up the four terms of step 4 :
                    (2x-7)  •  (2x-7)
             Which is the desired factorization
Multiplying Exponential Expressions :
 2.2    Multiply  (2x-7)  by  (2x-7)  
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is  (2x-7)  and the exponents are :
          1 , as  (2x-7)  is the same number as  (2x-7)1  
 and   1 , as  (2x-7)  is the same number as  (2x-7)1  
The product is therefore,  (2x-7)(1+1) = (2x-7)2  
Final result :
  (2x - 7)2