https://file.aiquickdraw.com/mathbot/file/1730551828958y9l18d4t.jpg

To solve this problem, we need to simplify the expression:

\[
m(2n - 3m) - n(3m - 1)
\]

### Step 1: Distribute each term
Let's expand each part separately:

1. Expanding \( m(2n - 3m) \):
   \[
   m(2n - 3m) = 2mn - 3m^2
   \]

2. Expanding \( -n(3m - 1) \):
   \[
   -n(3m - 1) = -3mn + n
   \]

### Step 2: Combine the terms
Now we put both expansions together:

\[
2mn - 3m^2 - 3mn + n
\]

### Step 3: Simplify by combining like terms
Combine \( 2mn \) and \( -3mn \):

\[
-3m^2 - mn + n
\]

### Final Answer
The simplified expression is:

\[
-3m^2 - mn + n
\]

### Answer Choice
This matches with option **B**:

\[
\boxed{-3m^2 - mn + n}
\]

Would you like further explanation on this process?

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Here are 5 related questions for practice:

1. Simplify \( a(b - c) - d(b - e) \).
2. Expand and simplify \( x(4y - 2x) - y(5x - 3) \).
3. If \( m = 2 \) and \( n = 3 \), what is the value of \( m(2n - 3m) - n(3m - 1) \)?
4. What are the steps for factoring an expression like \( -3m^2 - mn + n \)?
5. How can you check if your simplification is correct?

**Tip:** When simplifying expressions, keep track of signs carefully, especially when distributing negative terms.

Simplify the expression m(2n - 3m) - n(3m - 1) with a detailed step-by-step solution using algebraic techniques and the distributive property. Ideal for students in Grades 7-10.

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