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

Question

Responses

z2−8z−16
z squared minus 8 z minus 16

z(z)+4z(z)−4(4)
z left parenthesis z right parenthesis plus 4 z left parenthesis z right parenthesis minus 4 left parenthesis 4 right parenthesis

2z2−z2−8
2 z squared minus z squared minus 8

z2+4z−4z−16

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, \(a = z\) 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.