Solution - Simplification or other simple results

Step  1  :

Equation at the end of step  1  :

  ((22•32t2) -  24t) +  4

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   36t² - 24t + 4  =   4 • (9t² - 6t + 1) 

Trying to factor by splitting the middle term

 3.2     Factoring  9t² - 6t + 1 

The first term is,  9t²  its coefficient is  9 .
The middle term is,  -6t  its coefficient is  -6 .
The last term, "the constant", is  +1 

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

Step-2 : Find two factors of  9  whose sum equals the coefficient of the middle term, which is   -6 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  -3 
                     9t² - 3t - 3t - 1

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

Multiplying Exponential Expressions :

 3.3    Multiply  (3t-1)  by  (3t-1) 

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

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

Final result :

  4 • (3t - 1)2