Which polynomial represents the sum below? (16x2 - 16) + (-12x2 - 12x + 12) a. 4x2 - 12x + 28 b. 28x2 - 28x - 12 c. 16x2 - 28x - 16 d. 4x2 - 12x - 4

The correct answer is:  [D]:  " 4x² − 12x − 4 " .

Explanation: 

Given:

    "  (16x²  − 16)  +  ( -12x² − 12x + 12) " ;    Simplify.

Note the "distributive property of multiplication:

  a(b + c)  =  ab +  ac ; 

  a(b − c)  =  ab − ac .

So we can rewrite the expression as:

  "  (16x²  − 16)  +  1( -12x² − 12x + 12) "  ; 

{The "1" is implied; since "1", multiplied by any value, results in the exact same value.}.

Let us examine the following part of the expression:

    "  + 1 ( -12x² − 12x + 12 ) " ;

Using the distributive property of multiplication:
 
"  + 1 ( -12x² − 12x + 12 )  =  (1 * -12x²) − (1 * 12x) + (1 * 12) ; 

                                        =   "  − 12x² − 12x + 12 " ; 

Now, bring down the other part of the expression; & rewrite:

→   " (16x²  − 16)  − 12x² − 12x + 12 " ; 

   →  " 16x²  − 16 − 12x² − 12x + 12 "  ;

Now, combine the "like terms" :

     + 16x²  −  12x²  = 4x²  ; 

     − 16 + 12 =  -4 ; 

and we have " − 12x" ;

So we can rewrite the expression as:


 →   " 4x² − 12x − 4 " ; 

        →  which is:  "Answer choice:  [D]:  " 4x² − 12x − 4 " .

 

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