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To factor the expression \( 24a^5 + 18a^6 \), let's go through the steps:

### Step-by-Step Solution:
1. **Identify the Greatest Common Factor (GCF):**
   - The terms are \( 24a^5 \) and \( 18a^6 \).
   - The GCF of the coefficients (24 and 18) is 6.
   - The GCF of the variables \( a^5 \) and \( a^6 \) is \( a^5 \), as \( a^5 \) is the lowest power of \( a \).

2. **Factor out the GCF:**
   - The GCF of \( 24a^5 + 18a^6 \) is \( 6a^5 \).
   - Factoring out \( 6a^5 \):
     \[
     24a^5 + 18a^6 = 6a^5(4 + 3a)
     \]

### Final Answer:
The factored form of the expression is:
\[
6a^5(4 + 3a)
\]

Would you like more details, or do you have any questions about this solution?

### Further Questions:
1. How do you find the greatest common factor (GCF) of terms with variables?
2. What are the next steps if factoring leads to a quadratic or higher degree polynomial?
3. Can you factor an expression like \( 24a^5 - 18a^6 \), and if so, how does it differ?
4. How do you approach factoring when there are multiple variables in the expression?
5. What is the role of factoring in simplifying algebraic expressions?

**Tip:** Always start by factoring out the greatest common factor (GCF) in polynomial expressions—it simplifies the expression and can make further factoring easier!

Learn how to factor the algebraic expression 24a^5 + 18a^6 by factoring out the greatest common factor (GCF). This step-by-step solution simplifies the expression to 6a^5(4 + 3a). Suitable for Grades 9-12 students studying algebra.

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