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Let's solve the given product problem correctly. The expression provided is:

\[
(7z + 9)(12z - 5)
\]

We'll apply the distributive property (also known as FOIL when multiplying binomials) to expand this:

### Step 1: Multiply the first terms
\[
7z \cdot 12z = 84z^2
\]

### Step 2: Multiply the outer terms
\[
7z \cdot (-5) = -35z
\]

### Step 3: Multiply the inner terms
\[
9 \cdot 12z = 108z
\]

### Step 4: Multiply the last terms
\[
9 \cdot (-5) = -45
\]

### Step 5: Combine like terms
Now, we sum up all the terms:
\[
84z^2 + (-35z) + 108z + (-45)
\]

Simplifying the middle terms:
\[
84z^2 + 73z - 45
\]

So, the correct expanded form is:
\[
84z^2 + 73z - 45
\]

It looks like the expression you entered was incorrect because it involved an exponent of \(z^4\), but the product only involves terms with \(z^2\) and \(z\), along with constants.

Would you like more details on any part of this solution? 

Here are 5 related questions to expand on this topic:

1. How do you multiply binomials using the FOIL method?
2. What is the distributive property, and how does it apply to polynomial multiplication?
3. How do you simplify like terms when expanding polynomials?
4. How does this problem change if one of the terms has a higher exponent (e.g., \(z^3\))?
5. What are some common mistakes to avoid when multiplying polynomials?

### Tip:
When multiplying binomials, always ensure you multiply each term from the first binomial with each term from the second binomial, and carefully combine like terms!

Find the product. Collect all like terms. (7z + 9)(12z - 5)

Learn how to multiply and expand the binomials (7z + 9)(12z - 5) using the FOIL method and the distributive property. This solution covers polynomial multiplication, combining like terms, and is ideal for students in Grades 8-10.

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