https://file.aiquickdraw.com/mathbot/file/1726756686786tbr8m8if.jpg

The problem in the image asks:

"Which of the following expressions is equivalent to \((n+9)(n-2)\)?"

To solve this, we need to expand the binomial expression:

\[
(n+9)(n-2)
\]

Using the distributive property (FOIL method):

\[
n(n) + n(-2) + 9(n) + 9(-2)
\]
\[
= n^2 - 2n + 9n - 18
\]
\[
= n^2 + 7n - 18
\]

So, the expression \((n+9)(n-2)\) simplifies to:

\[
n^2 + 7n - 18
\]

The correct answer is option **(4): \( n^2 + 7n - 18 \)**.

Would you like further details, or have any questions? 

Here are five related questions to explore further:
1. How do you apply the FOIL method for expanding binomials?
2. What are the steps to simplify expressions with multiple terms?
3. How do you factor quadratic expressions like \( n^2 + 7n - 18 \)?
4. How does the distributive property help in multiplying binomials?
5. What are common mistakes to avoid when expanding binomials?

**Tip:** Always check if the terms in a quadratic expression can be simplified further or factored.

Which of the following expressions is equivalent to (n+9)(n-2)?

Explore the step-by-step solution to the quadratic expression (n+9)(n-2) using the FOIL method. This detailed explanation helps students in Grades 7-9 understand binomial expansion and algebraic simplifications.

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