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

Question

Responses

z2−8z−16

2z2−z2−8

z(z)+4z(z)−4(4)

z2+4z−4z−16

Answer 1

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

Here, we can identify \(a = z\) and \(b = 4\):

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

Now, let's analyze the given options:

1. \(z^2 - 8z - 16\)
2. \(2z^2 - z^2 - 8\)
3. \(z(z) + 4z(z) - 4(4)\)
4. \(z^2 + 4z - 4z - 16\)

The correct simplified expression from our calculation is \(z^2 - 16\).

Now checking the options:

1. \(z^2 - 8z - 16\) does not match.
2. \(2z^2 - z^2 - 8\) simplifies to \(z^2 - 8\), which does not match.
3. \(z(z) + 4z(z) - 4(4)\) does not simplify to \(z^2 - 16\).
4. \(z^2 + 4z - 4z - 16\) can be simplified to \(z^2 - 16\), which matches our result.

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

\(z^2 + 4z - 4z - 16\).