Let's solve the expression step by step to factor and simplify it.

Given expression:

\[
6x^2y^2 + 3xy^3 - 3xy^2
\]

### Step 1: Identify the Greatest Common Factor (GCF)
First, let's find the GCF of the terms. 

- The terms are \(6x^2y^2\), \(3xy^3\), and \(3xy^2\).
- The common factor in all terms is \(3xy^2\).

### Step 2: Factor out the GCF
Now, we factor \(3xy^2\) out of each term:

\[
6x^2y^2 + 3xy^3 - 3xy^2 = 3xy^2(2x) + 3xy^2(y) - 3xy^2(1)
\]

This simplifies to:

\[
3xy^2(2x + y - 1)
\]

### Final Solution
The factored form of the expression is:

\[
\boxed{3xy^2(2x + y - 1)}
\]

This is the fully factored and simplified form of the given expression.

Would you like more details or have any questions?

### Related Questions:
1. How do you verify that the factorization is correct?
2. What are the different methods for factoring polynomials?
3. How can you factor trinomials where the leading coefficient is greater than 1?
4. What are common mistakes to avoid when factoring?
5. How do you solve equations after factoring polynomials?

### Tip:
Always double-check your factorization by expanding the factored expression back to the original form to ensure accuracy.

Learn how to factor and simplify the polynomial expression 6x^2y^2 + 3xy^3 - 3xy^2 with a step-by-step solution. This problem covers polynomial factorization and simplification techniques. Suitable for students in Grades 9-12.

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