Answer :
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]
[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]
