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:

$z^2-16$.