I have no idea how to do this problem.

Find the product:

z squared plus 7z-8 z sqaured-8z
------------------- X __________
z squared-64 z-1

I think I see something like

(z^2 + 7z - 8)/(z^2 - 64)* (x^2 - 8z)/(z-1)

if so, I see after it factors nicely .

=(z+8)(z-1)/((z-8)(z+8)) * z(z-8)/(z-1)
= z but z ≠ 1,±8

Oh yes I forgot to add the choices are... z or -z or z over z-1 or z over z+1

To find the product, we need to multiply the two expressions. Let's break down the process step by step:

First, let's simplify the expression on the left-hand side:
z^2 + 7z - 8 / (z^2 - 64)

Next, let's simplify the expression on the right-hand side:
(z^2 - 8z) / (z - 1)

To multiply these two expressions, we can cancel out common factors in the numerator and denominator:
(z^2 + 7z - 8) / (z^2 - 64) * (z^2 - 8z) / (z - 1)

Now, let's factorize the expressions and simplify further where possible:
[(z + 8)(z - 1)] / [(z - 8)(z + 8)] * [(z)(z - 8)] / (z - 1)

We can see that the expression (z - 1) appears in both the numerator and denominator, so we can cancel it out:
[(z + 8) * 1] / [(z - 8) * (z + 8)] * [z * (z - 8)] / 1

Now, let's multiply the remaining terms in the numerator and denominator:
[z * (z - 1)] / (z - 8)

Finally, we can write the product in its simplified form:
z(z - 1) / (z - 8)

That's the solution to the problem.