https://file.aiquickdraw.com/mathbot/file/1730743883687v06jk7e5.jpg

To solve this problem, we need to expand the expression \((w - 8)(w + 10)\).

### Step-by-Step Solution

1. **Distribute** each term in the first binomial with each term in the second binomial:
   \[
   (w - 8)(w + 10) = w \cdot w + w \cdot 10 - 8 \cdot w - 8 \cdot 10
   \]

2. **Calculate each multiplication**:
   - \(w \cdot w = w^2\)
   - \(w \cdot 10 = 10w\)
   - \(-8 \cdot w = -8w\)
   - \(-8 \cdot 10 = -80\)

3. **Combine the results**:
   \[
   w^2 + 10w - 8w - 80
   \]

4. **Simplify by combining like terms** (\(10w - 8w\)):
   \[
   w^2 + 2w - 80
   \]

### Final Answer
The expression that is equivalent to \((w - 8)(w + 10)\) is:
\[
w^2 + 2w - 80
\]

So, the correct option is **\(w^2 + 2w - 80\)**.

Would you like more details on any specific step, or have any other questions?

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Here are five related questions to further your understanding:
1. How do you expand a binomial product in general?
2. What are like terms, and why can we combine them?
3. What would change if the signs in one of the terms were reversed, like \((w + 8)(w + 10)\)?
4. How would this process change for an expression like \((w - 8)(w - 10)\)?
5. What are some practical applications of expanding binomials?

**Tip:** Always look for common terms to combine in your final steps to simplify polynomial expressions.

The expression that is equivalent to \((w - 8)(w + 10)\) is?

Learn how to expand the binomial expression (w - 8)(w + 10) using the distributive property. This problem demonstrates polynomial expansion with a detailed solution, suitable for Algebra students in Grade 9.

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