Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (3a2 +  4a) +  1

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3a²+4a+1 

The first term is,  3a²  its coefficient is  3 .
The middle term is,  +4a  its coefficient is  4 .
The last term, "the constant", is  +1 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 1 = 3 

Step-2 : Find two factors of  3  whose sum equals the coefficient of the middle term, which is   4 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  1  and  3 
                     3a² + 1a + 3a + 1

Step-4 : Add up the first 2 terms, pulling out like factors :
                    a • (3a+1)
              Add up the last 2 terms, pulling out common factors :
                     1 • (3a+1)
Step-5 : Add up the four terms of step 4 :
                    (a+1)  •  (3a+1)
             Which is the desired factorization

Final result :

  (3a + 1) • (a + 1)