Which expression is equivalent to (z+4)(z−4)?(1 point)

To simplify the expression \((z+4)(z−4)\), we can use the difference of squares formula, which states that \((a + b)(a - b) = a^2 - b^2\).

Here, \(a = z\) and \(b = 4\).

So we have:

\[
(z + 4)(z - 4) = z^2 - 4^2 = z^2 - 16
\]

Now, let's evaluate the choices provided:

1. **z² - 8z - 16**: This is incorrect.
2. **z(z) + 4z(z) - 4(4)**: This simplifies to \(z^2 + 4z^2 - 16\), which is also incorrect.
3. **2z² - z² - 8**: This simplifies to \(z² - 8\), which is incorrect.
4. **z² + 4z - 4z - 16**: This simplifies to \(z² + 0 - 16 = z² - 16\), which is correct.

Thus, the equivalent expression to \((z+4)(z−4)\) is:

**z² - 16**.

The closest option is **z² + 4z - 4z - 16**, which simplifies to **z² - 16**.