The expression \((z+4)(z−4)\) can be simplified using the difference of squares formula, which states that \( (a+b)(a-b) = a^2 - b^2 \).
In this case:
- \( a = z \)
- \( b = 4 \)
So, applying the formula:
\[ (z+4)(z-4) = z^2 - 4^2 = z^2 - 16 \]
Thus, the equivalent expression is \( z^2 - 16 \).
However, from the responses you've provided, if none match that exactly, there might be confusion. From the choices you have:
- \( z^2 - 8z - 16 \)
- \( 2z^2 - z^2 - 8 \)
Neither matches the correct answer exactly, which is simply \( z^2 - 16 \).
If you need to select from the given options, none of them are correct, as neither expression represents \((z+4)(z−4)\) correctly.