https://file.aiquickdraw.com/mathbot/file/1729723589891daw09q6m.jpg

The problem in the image is:

\[
(v - 3)(4v^2 - 5v - 5)
\]

To simplify this, we'll use the distributive property (also called FOIL for binomials):

### Step-by-Step Process:

1. **Distribute \(v\):**
   \[
   v(4v^2 - 5v - 5) = 4v^3 - 5v^2 - 5v
   \]

2. **Distribute \(-3\):**
   \[
   -3(4v^2 - 5v - 5) = -12v^2 + 15v + 15
   \]

3. **Combine like terms:**
   \[
   4v^3 - 5v^2 - 5v - 12v^2 + 15v + 15
   \]
   Group the terms:
   \[
   4v^3 + (-5v^2 - 12v^2) + (-5v + 15v) + 15
   \]
   Simplify:
   \[
   4v^3 - 17v^2 + 10v + 15
   \]

### Final Answer:
\[
4v^3 - 17v^2 + 10v + 15
\]

Let me know if you need further details or have any questions! 

Here are 5 related questions you can explore:
1. How would the result change if the first term was \( (v + 3) \) instead of \( (v - 3) \)?
2. How do you factor polynomials like \( 4v^3 - 17v^2 + 10v + 15 \)?
3. Can this expression be simplified further by factoring or other means?
4. What is the degree of the final polynomial?
5. How does the distributive property work for more complex polynomials?

**Tip:** Always combine like terms carefully to avoid mistakes when simplifying!

Learn how to simplify the binomial expression (v - 3)(4v^2 - 5v - 5) using the distributive property. This solution involves distributing terms, combining like terms, and simplifying the polynomial. Suitable for students in Grades 9-12.

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