Using an example that you make up, explain how to factor out the GCF or pick a question that is a difference of 2 squares and explain how to factor it. You do not have to do both. Also, leave another question for your classmates to answer as part of their responses. 

Let's go with an example involving factoring out the Greatest Common Factor (GCF).

### Example:

Factor the following expression by factoring out the GCF:

\[
12x^3 + 18x^2 - 24x
\]

### Step-by-Step Explanation:

1. **Identify the GCF of the coefficients**:
   - The coefficients are 12, 18, and 24. The GCF of these three numbers is **6**.

2. **Identify the GCF of the variables**:
   - The variable part consists of \(x^3\), \(x^2\), and \(x\). The GCF of these is the smallest power of \(x\), which is **\(x\)**.

3. **Factor out the GCF**:
   - Now that we know the GCF is \(6x\), we factor that out from each term in the expression:
   \[
   12x^3 + 18x^2 - 24x = 6x(2x^2 + 3x - 4)
   \]

4. **Check your work**:
   - To verify, distribute the \(6x\) back through the factored expression:
     \[
     6x(2x^2 + 3x - 4) = 12x^3 + 18x^2 - 24x
     \]
   - Since this matches the original expression, the factorization is correct.

### Final Answer:
\[
12x^3 + 18x^2 - 24x = 6x(2x^2 + 3x - 4)
\]

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### Question for your classmates:

Factor the following expression, which is a difference of two squares:

\[
9x^2 - 25
\]

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Would you like more details on GCF or factoring methods? Here are some additional questions you can explore:

1. How do you factor quadratic expressions that don't have a common factor?
2. What is the difference between factoring completely and factoring by grouping?
3. Can you explain the steps to factor a trinomial with a leading coefficient greater than 1?
4. How would you factor the expression \(x^4 - 16\)?
5. What happens when you factor an expression that can't be simplified further?

**Tip:** Always check your factorization by distributing the factors back to make sure the expression equals the original.

Using an example that you make up, explain how to factor out the GCF or pick a question that is a difference of 2 squares and explain how to factor it. You do not have to do both. Also, leave another question for your classmates to answer as part of their responses.

Learn how to factor algebraic expressions by factoring out the greatest common factor (GCF) or using the difference of squares method. This detailed guide provides step-by-step solutions, formulas, and examples, including factoring 12x^3 + 18x^2 - 24x. Suitable for students in Grades 9-10.

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