To factor the expression \(18x^2 + 27x\), follow these steps:

1. **Identify the common factors**:  
   The terms \(18x^2\) and \(27x\) share a common factor. The greatest common factor (GCF) of 18 and 27 is 9, and both terms also have an \(x\) in common.

2. **Factor out the GCF**:  
   Factor 9x out of the expression:
   \[
   18x^2 + 27x = 9x(2x + 3)
   \]

So, the factored form of \(18x^2 + 27x\) is \(9x(2x + 3)\).

Would you like more details or have any questions?

Here are some related questions you might find useful:

1. How do you find the greatest common factor of two terms?
2. How do you know when you've completely factored an expression?
3. What is the difference between factoring and expanding an expression?
4. How would you factor a trinomial, such as \(ax^2 + bx + c\)?
5. What role does factoring play in solving quadratic equations?

**Tip**: When factoring expressions with variables, always look for the highest power of the variable that can be factored out from all terms.

Learn how to factor the expression 18x^2 + 27x using the greatest common factor (GCF) method with a detailed step-by-step solution. This problem covers key algebraic concepts such as factoring quadratic expressions. Suitable for students in Grades 7-9.

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