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Let's simplify the expression \((6n - 5)(n + 4)\) to determine which answer is correct.

We can use the distributive property (FOIL method) to expand the product:

\[
(6n - 5)(n + 4) = 6n(n) + 6n(4) - 5(n) - 5(4)
\]

Now calculate each term:

\[
6n(n) = 6n^2
\]
\[
6n(4) = 24n
\]
\[
-5(n) = -5n
\]
\[
-5(4) = -20
\]

Now, combine the like terms:

\[
6n^2 + 24n - 5n - 20 = 6n^2 + 19n - 20
\]

The simplified expression is \(6n^2 + 19n - 20\), which corresponds to option **K**.

Would you like a more detailed explanation on any step?

Here are 5 related questions to explore:

1. What is the FOIL method, and how is it applied in polynomial multiplication?
2. How do you expand binomials using the distributive property?
3. Can you simplify the expression \((3n + 2)(n - 1)\) using the same technique?
4. What happens if you expand more complex polynomials, such as \((2x^2 + 3)(x + 4)\)?
5. How would you factor a quadratic expression like \(6n^2 + 19n - 20\)?

**Tip**: Always combine like terms after expanding an expression to ensure you have the simplest form.

The expression (6n - 5)(n + 4) is equivalent to:

Learn how to expand and simplify the polynomial expression (6n - 5)(n + 4) using the distributive property. The problem involves applying algebraic concepts and simplifying terms to find the equivalent expression, suitable for students in Grades 7-9.

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