Let's simplify the given expression step by step:

Given expression:  
\[ (m - 2n)(m + 1) - 3m(m - 2n) \]

1. **Expand the first term** \((m - 2n)(m + 1)\):
   \[
   (m - 2n)(m + 1) = m(m + 1) - 2n(m + 1)
   \]
   \[
   = m^2 + m - 2nm - 2n
   \]
   So, \((m - 2n)(m + 1) = m^2 + m - 2nm - 2n\).

2. **Expand the second term** \(-3m(m - 2n)\):
   \[
   -3m(m - 2n) = -3m^2 + 6mn
   \]

3. **Combine all the terms**:
   \[
   (m^2 + m - 2nm - 2n) - (3m^2 - 6mn)
   \]
   Distribute the negative sign:
   \[
   = m^2 + m - 2nm - 2n - 3m^2 + 6mn
   \]

4. **Combine like terms**:
   \[
   = (m^2 - 3m^2) + (m + 6mn - 2nm) - 2n
   \]
   \[
   = -2m^2 + (m + 4mn) - 2n
   \]

So, the simplified expression is:  
\[
-2m^2 + m + 4mn - 2n
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Simplify \( (x - y)(x + y) - 2x(x - y) \).
2. Expand and simplify \( (a + 3b)(a - 2) - 4a(a + 3b) \).
3. Factor \( -2m^2 + m + 4mn - 2n \).
4. Simplify \( (p - q)(p + r) - 5p(p - q) \).
5. Combine like terms in \( -4x^2 + 3x + 7xy - 2x^2 - 2x + 5xy \).

**Tip:** Always expand the expressions fully before combining like terms to ensure the correct simplification.

Learn how to simplify the expression (m - 2n)(m + 1) - 3m(m - 2n) step-by-step with detailed explanations. This problem involves algebraic simplification and distribution of terms, suitable for students in Grades 7-9.

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