Answer:

Step-by-step explanation:
 (((4x-9)•(((2•(x2))+2x)+1))•(4x-9))•((2x2+2x)+1)
]  (((4x-9)•((2x2+2x)+1))•(4x-9))•(2x2+2x+1)
Trying to factor by splitting the middle term
Factoring  2x2+2x+1 
The first term is,  2x2  its coefficient is  2 .
The middle term is,  +2x  its coefficient is  2 .
The last term, "the constant", is  +1 
Step-1 : Multiply the coefficient of the first term by the constant   2 • 1 = 2 
Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   2 .
      -2    +    -1    =    -3	
      -1    +    -2    =    -3	
      1    +    2    =    3	
      2    +    1    =    3	
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
  ((4x-9)•(2x2+2x+1)•(4x-9))•(2x2+2x+1)
Multiplying Exponential Expressions:
 4.1    Multiply  (4x-9)  by  (4x-9) 
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is  (4x-9)  and the exponents are :
          1 , as  (4x-9)  is the same number as  (4x-9)1 
 and   1 , as  (4x-9)  is the same number as  (4x-9)1 
The product is therefore,  (4x-9)(1+1) = (4x-9)2 
Trying to factor by splitting the middle term
 5.1     Factoring  2x2+2x+1 
The first term is,  2x2  its coefficient is  2 .
The middle term is,  +2x  its coefficient is  2 .
The last term, "the constant", is  +1 
Step-1 : Multiply the coefficient of the first term by the constant   2 • 1 = 2 
Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   2 .
      -2    +    -1    =    -3	
      -1    +    -2    =    -3	
      1    +    2    =    3	
      2    +    1    =    3	
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Multiplying Exponential Expressions:
 5.2    Multiply  (2x2+2x+1)  by  (2x2+2x+1) 
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is  (2x2+2x+1)  and the exponents are :
       1 , as  (2x2+2x+1)  is the same number as  (2x2+2x+1)1 
 and   1 , as  (2x2+2x+1)  is the same number as  (2x2+2x+1)1 
The product is therefore,  (2x2+2x+1)(1+1) = (2x2+2x+1)2 
Final result :
  (4x - 9)2 • (2x2 + 2x + 1)2