Question

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

Answer 1

The correct answer is: [D]: " 4x² − 12x − 4 " .
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Explanation:
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Given:
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" (16x² − 16) + ( -12x² − 12x + 12) " ; Simplify.
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Note the "distributive property of multiplication:
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a(b + c) = ab + ac ;

a(b − c) = ab − ac .
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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:
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" + 1 ( -12x² − 12x + 12 ) " ;

Using the distributive property of multiplication:

" + 1 ( -12x² − 12x + 12 ) = (1 * -12x²) − (1 * 12x) + (1 * 12) ;

= " − 12x² − 12x + 12 " ;
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Now, bring down the other part of the expression; & rewrite:
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→ " (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:
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→ " 4x² − 12x − 4 " ;

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