The two algebraic expressions you provided are \( 9a^2b^2 \) and \( 18a^2b \). 

Here’s a breakdown:

### 1. **Like Terms**: 
These two expressions are **not** like terms because the variables are not raised to the same powers. Specifically:
- In \( 9a^2b^2 \), the exponent of \( b \) is 2.
- In \( 18a^2b \), the exponent of \( b \) is 1.

### 2. **Greatest Common Factor (GCF)**:
Even though these terms are not like terms, they share some common factors:
- The common factor in the coefficients is 9.
- Both terms have \( a^2 \) as a common factor.
- Both terms have at least one factor of \( b \).

So, the GCF of these two terms is \( 9a^2b \).

### 3. **Factorization**:
You can factor out the GCF from both terms:
\[
9a^2b^2 - 18a^2b = 9a^2b(b - 2)
\]

This is the factorized form of the expression.

### Summary:
- \( 9a^2b^2 \) and \( 18a^2b \) are not like terms and cannot be directly added or subtracted.
- They share a GCF of \( 9a^2b \), which allows you to factor the expression as \( 9a^2b(b - 2) \).

Would you like more details, or do you have any other questions?

Here are 5 related questions:

1. How do you determine the greatest common factor (GCF) of algebraic expressions?
2. What is the process of factoring expressions with multiple variables?
3. How do you factor expressions when the terms are not like terms?
4. Can you simplify expressions with different exponents on the same variable?
5. What are the steps to expand a factorized algebraic expression?

**Tip**: Always check the exponents of variables when determining if terms are like terms—they must match exactly!

Explore the algebraic expressions 9a²b² and 18a²b, understanding their differences and how to find the Greatest Common Factor (GCF) and factorize them. This detailed explanation covers key concepts in algebra and is suitable for Grades 7-9.

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