https://file.aiquickdraw.com/mathbot/file/1727214120653vvne0wg1.jpg

The expression in the image is \((n^2 + 5)(n - 8)\).

To expand this expression, we can apply the distributive property, which involves multiplying each term in \((n^2 + 5)\) by each term in \((n - 8)\).

Let's solve this step by step:

\[
(n^2 + 5)(n - 8) = n^2(n) + n^2(-8) + 5(n) + 5(-8)
\]

Now, simplify each term:

\[
= n^3 - 8n^2 + 5n - 40
\]

Thus, the expanded form of the expression is:

\[
n^3 - 8n^2 + 5n - 40
\]

Would you like further details or explanations on any part of this process?

Here are 5 related questions to expand on this topic:
1. How do you factor a cubic expression like \(n^3 - 8n^2 + 5n - 40\)?
2. What are the uses of polynomial expansions in real-world applications?
3. How does the distributive property work in polynomial multiplication?
4. What are the different methods to simplify polynomials?
5. How can you graph a cubic polynomial such as \(n^3 - 8n^2 + 5n - 40\)?

**Tip:** When expanding expressions, make sure to distribute every term in the first set of parentheses to every term in the second set.

Learn how to expand the polynomial expression (n^2 + 5)(n - 8) using the distributive property. This algebra problem involves multiplying a binomial and a trinomial, with a detailed step-by-step solution for students in Grades 8-10.

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