To simplify the expression \((4k + 2m + n) - (3m - 4n - 2k)\), follow these steps:

1. Distribute the negative sign through the parentheses.
2. Combine like terms.

**Step 1: Distribute the negative sign**

\[
(4k + 2m + n) - (3m - 4n - 2k)
\]

Distribute the negative sign to the second group:

\[
(4k + 2m + n) - 3m + 4n + 2k
\]

**Step 2: Combine like terms**

Group the \(k\) terms together, the \(m\) terms together, and the \(n\) terms together:

\[
(4k + 2k) + (2m - 3m) + (n + 4n)
\]

Combine the \(k\) terms:

\[
4k + 2k = 6k
\]

Combine the \(m\) terms:

\[
2m - 3m = -m
\]

Combine the \(n\) terms:

\[
n + 4n = 5n
\]

So, the simplified expression is:

\[
6k - m + 5n
\]

Do you want more details or have any questions about this process?

Here are 5 numbered questions you can ask:

1. How do you distribute a negative sign in algebraic expressions?
2. What are the steps to combine like terms?
3. How can you simplify expressions with multiple variables?
4. Can you explain how to solve polynomial equations?
5. How do you approach solving complex algebraic expressions?

**Tip:** When simplifying expressions, carefully distribute negative signs and group like terms to ensure accuracy.

Learn how to simplify the algebraic expression (4k + 2m + n) - (3m - 4n - 2k) step-by-step with detailed explanations. This problem involves combining like terms and applying the distributive property, suitable for students in Grades 7-9.

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