Certainly! Let's simplify the expression [tex]\(\left(x^2 + 16\right)\left(x^2 - 16\right)\)[/tex] step-by-step.
First, notice that we have a product of two binomials, [tex]\((x^2 + 16)\)[/tex] and [tex]\((x^2 - 16)\)[/tex]. This is in the form of [tex]\((a + b)(a - b)\)[/tex], which can be simplified using the difference of squares formula:
[tex]\[
(a + b)(a - b) = a^2 - b^2
\][/tex]
In our expression, [tex]\(a = x^2\)[/tex] and [tex]\(b = 16\)[/tex]. Applying the difference of squares formula:
[tex]\[
(x^2 + 16)(x^2 - 16) = (x^2)^2 - 16^2
\][/tex]
Now, calculating each part:
1. [tex]\((x^2)^2\)[/tex] simplifies to [tex]\(x^4\)[/tex]
2. [tex]\(16^2\)[/tex] simplifies to [tex]\(256\)[/tex]
Substituting these back into the equation:
[tex]\[
(x^2)^2 - 16^2 = x^4 - 256
\][/tex]
So, the simplified expression is:
[tex]\[
x^4 - 256
\][/tex]
Therefore, the best answer is:
A. [tex]\(x^4 - 256\)[/tex]
