Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  (32x2 -  24x) +  16

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  9x²-24x+16 

The first term is,  9x²  its coefficient is  9 .
The middle term is,  -24x  its coefficient is  -24 .
The last term, "the constant", is  +16 

Step-1 : Multiply the coefficient of the first term by the constant   9 • 16 = 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 
                     9x² - 12x - 12x - 16

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

Multiplying Exponential Expressions :

 2.2    Multiply  (3x-4)  by  (3x-4) 

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

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

Final result :

  (3x - 4)2