To simplify [tex]\((x^2 + 16)(x^2 - 16)\)[/tex], we can start by recognizing that this expression is a difference of squares. The difference of squares formula is given by:
[tex]\[
(a^2 - b^2) = (a - b)(a + b)
\][/tex]
In this case, we let [tex]\(a = x^2\)[/tex] and [tex]\(b = 16\)[/tex]. Applying the difference of squares formula, we get:
[tex]\[
(x^2 + 16)(x^2 - 16) = (x^2)^2 - (16)^2
\][/tex]
Now, we simplify each term:
[tex]\[
(x^2)^2 = x^4
\][/tex]
[tex]\[
(16)^2 = 256
\][/tex]
Substituting these back into the expression, we obtain:
[tex]\[
(x^2 + 16)(x^2 - 16) = x^4 - 256
\][/tex]
Therefore, the simplified form of [tex]\((x^2 + 16)(x^2 - 16)\)[/tex] is [tex]\(x^4 - 256\)[/tex].
The best answer is:
D. [tex]\(x^4 - 256\)[/tex]
