The expression you provided is:

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

This expression can be factored by identifying common factors in each term.

### Step 1: Identify the Greatest Common Factor (GCF)
The greatest common factor for all three terms is \( 3xy^2 \).

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

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

So the factored form of the expression is:

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

This is the simplified factored expression.

Would you like more details or have any questions?

### Related Questions:
1. How do you determine the greatest common factor (GCF) in a polynomial?
2. What is the difference between factoring and expanding polynomials?
3. Can all polynomials be factored by grouping? 
4. How do you factor polynomials with more than three terms?
5. What are special cases in polynomial factoring, like perfect square trinomials?

### Tip:
When factoring polynomials, always start by looking for the greatest common factor (GCF) before attempting other methods like grouping or using special formulas.

Learn how to factor the polynomial 6x^2y^2 + 3xy^3 - 3xy^2 with a step-by-step solution. This problem involves identifying the greatest common factor (GCF) and applying factoring techniques in polynomials. Suitable for students in Grades 9-12.

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