Question

Which expression is equivalent to (z+4) (z-4)?
A. Z²+4z-4z-16
B. 2z²-z²-8
C. Z²-8z-16
D. Z(z)+4z(z)-4(4)

Answer 1

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 \( z^2 - 16 \).