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.