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Which expression is equivalent to (z+4)(z−4) ?(1 point) Responses 2z2−z2−8 2 z squared minus z squared minus 8 z2+4z−4z−16 z squared plus 4 z minus 4 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 z2−8z−16

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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 get:

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

Now let's compare this with the options given:

  1. \(2z^2 - z^2 - 8\) simplifies to \(z^2 - 8\), which is not equivalent.
  2. \(z^2 + 4z - 4z - 16\) simplifies to \(z^2 - 16\), which is equivalent.
  3. \(z(z) + 4z(z) - 4(4)\) expands to \(z^2 + 4z^2 - 16\), which simplifies to \(5z^2 - 16\), not equivalent.
  4. \(z^2 - 8z - 16\) is not equivalent either.

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

\(z^2 - 16\)

So, the correct response from the options is: \(z^2 + 4z - 4z - 16\).