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

Answer 1

To find an expression equivalent to \((z + 4)(z - 4)\), we can use the difference of squares formula, which states:

\[ (a + b)(a - b) = a^2 - b^2 \]

In this case, \(a = z\) and \(b = 4\). Therefore, we can apply the formula as follows:

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

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

\[ z^2 - 16 \]

None of the responses provided directly state \(z^2 - 16\) as an option, but we can see that it is the difference of squares and can be properly simplified. It appears that responses may be presented in a confusing way, but the equivalent expression you are looking for is:

\(z^2 - 16\).