Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (24w2 -  24w) +  9

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  16w²-24w+9 

The first term is,  16w²  its coefficient is  16 .
The middle term is,  -24w  its coefficient is  -24 .
The last term, "the constant", is  +9 

Step-1 : Multiply the coefficient of the first term by the constant   16 • 9 = 144 

Step-2 : Find two factors of  144  whose sum equals the coefficient of the middle term, which is   -24 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -12  and  -12 
                     16w² - 12w - 12w - 9

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

Multiplying Exponential Expressions :

 2.2    Multiply  (4w-3)  by  (4w-3) 

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

In our case, the common base is  (4w-3)  and the exponents are :
          1 , as  (4w-3)  is the same number as  (4w-3)¹ 
 and   1 , as  (4w-3)  is the same number as  (4w-3)¹ 
The product is therefore,  (4w-3)⁽¹⁺¹⁾ = (4w-3)² 

Final result :

  (4w - 3)2