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Let's factor the expression \( 12n^2 - 9n^3 \).

### Step-by-step solution:

1. **Identify the greatest common factor (GCF)**:
   The GCF of the coefficients \(12\) and \(9\) is \(3\), and the lowest power of \(n\) common to both terms is \(n^2\).
   
   So, the GCF is \( 3n^2 \).

2. **Factor out the GCF**:
   \[
   12n^2 - 9n^3 = 3n^2(4 - 3n)
   \]

Thus, the factored form of \( 12n^2 - 9n^3 \) is:

\[
3n^2(4 - 3n)
\]

Would you like more details on any of the steps? 

Here are some related questions to explore:

1. What happens if the GCF is not factored out correctly?
2. How do we factor expressions with more than two terms?
3. Can you factor higher degree polynomials using the same method?
4. What are other factoring methods apart from finding the GCF?
5. How does factoring help in solving equations?

**Tip**: Always check by expanding your factors to ensure they simplify back to the original expression!

Learn how to factor the algebraic expression 12n^2 - 9n^3 step-by-step, using the greatest common factor (GCF). This example explores key algebra concepts suitable for Grades 8-10 students.

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