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, we have:
- \( a = z \)
- \( b = 4 \)
Applying the formula: \[ (z + 4)(z - 4) = z^2 - 4^2 = z^2 - 16 \]
Now, let's compare this result with the provided options:
A. \( z^2 + 4z - 4z - 16 \) simplifies to \( z^2 - 16 \) (this is equivalent). B. \( 2z^2 - z^2 - 8 \) simplifies to \( z^2 - 8 \) (not equivalent). C. \( z^2 - 8z - 16 \) (not equivalent). D. \( z(z) + 4z(z) - 4(4) \) simplifies to \( z^2 + 4z^2 - 16 \), which is not correct.
The answer is: A. \( z^2 + 4z - 4z - 16 \) which simplifies to \( z^2 - 16 \).