Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (72x2 +  70x) +  25

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  49x²+70x+25 

The first term is,  49x²  its coefficient is  49 .
The middle term is,  +70x  its coefficient is  70 .
The last term, "the constant", is  +25 

Step-1 : Multiply the coefficient of the first term by the constant   49 • 25 = 1225 

Step-2 : Find two factors of  1225  whose sum equals the coefficient of the middle term, which is   70 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  35  and  35 
                     49x² + 35x + 35x + 25

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

Multiplying Exponential Expressions :

 2.2    Multiply  (7x+5)  by  (7x+5) 

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

In our case, the common base is  (7x+5)  and the exponents are :
          1 , as  (7x+5)  is the same number as  (7x+5)¹ 
 and   1 , as  (7x+5)  is the same number as  (7x+5)¹ 
The product is therefore,  (7x+5)⁽¹⁺¹⁾ = (7x+5)² 

Final result :

  (7x + 5)2