The expression you've provided is \( 27x^2 + 9x \).

This expression can be factored by finding the greatest common factor (GCF) of the terms. Here's how you can factor it:

1. **Identify the GCF**: The GCF of \( 27x^2 \) and \( 9x \) is \( 9x \).

2. **Factor out the GCF**:
   \[
   27x^2 + 9x = 9x(3x + 1)
   \]

So, the factored form of the expression is \( \boxed{9x(3x + 1)} \).

Would you like more details or have any questions?

Here are five related questions:
1. How do you factor a trinomial?
2. What is the difference between factoring and expanding an expression?
3. How do you find the GCF of a set of terms?
4. Can you solve the equation \( 27x^2 + 9x = 0 \)?
5. What are the applications of factoring in solving quadratic equations?

**Tip:** Always start by factoring out the greatest common factor (GCF) before attempting other factoring methods.

Learn how to factor the algebraic expression 27x^2 + 9x by finding and factoring out the greatest common factor (GCF). This problem covers key algebra concepts, including GCF and factoring, suitable for students in Grades 7-9.

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