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Which polynomial represents the sum below?

[tex]\[
\left(16 x^2-16\right)+\left(-12 x^2-12 x+12\right)
\][/tex]

A. [tex]\(28 x^2-28 x-12\)[/tex]
B. [tex]\(4 x^2-12 x-4\)[/tex]
C. [tex]\(16 x^2-28 x-16\)[/tex]
D. [tex]\(4 x^2-12 x+28\)[/tex]


Sagot :

To determine which polynomial represents the sum of the given polynomials
[tex]\[ \left(16 x^2 - 16 \right) + \left( -12 x^2 - 12 x + 12 \right), \][/tex]
we need to combine like terms from each polynomial.

1. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ 16x^2 + (-12x^2) = 16x^2 - 12x^2 = 4x^2 \][/tex]

2. Combine the [tex]\(x\)[/tex] terms:
The first polynomial does not have an [tex]\(x\)[/tex] term, so we take the [tex]\(x\)[/tex] term from the second polynomial:
[tex]\[ -12x \][/tex]

3. Combine the constant terms:
[tex]\[ -16 + 12 = -4 \][/tex]

Putting it all together, the sum of the polynomials is:
[tex]\[ 4x^2 - 12x - 4 \][/tex]

Thus, the correct polynomial representing the sum is:
[tex]\[ \boxed{4x^2 - 12x - 4} \][/tex]

So the answer is:
[tex]\[ \text{B. } 4 x^2 - 12 x - 4 \][/tex]
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