To factor the polynomial \( 6xy^2 - 12x^2y \), let's go through the steps:

### 1. Identify the Greatest Common Factor (GCF):
First, we look for the greatest common factor (GCF) of the terms in the polynomial.

- The coefficients are 6 and 12. The GCF of 6 and 12 is 6.
- For the variables:
  - Both terms have the variable \(x\), with the smallest power being \(x\).
  - Both terms have the variable \(y\), with the smallest power being \(y\).

Thus, the GCF of the polynomial is \( 6xy \).

### 2. Factor out the GCF:
We factor \( 6xy \) out of each term in the polynomial:

\[
6xy^2 - 12x^2y = 6xy(y - 2x)
\]

### Final Answer:
The factored form of the polynomial \( 6xy^2 - 12x^2y \) is:

\[
6xy(y - 2x)
\]

Would you like further explanation on this or have any additional questions?

Here are 5 related questions you might explore next:
1. How do you factor a polynomial with three terms (a trinomial)?
2. What is the difference between factoring and expanding an expression?
3. How do you determine the GCF of multiple terms in a polynomial?
4. How can you factor polynomials with variables raised to higher powers, like cubes?
5. What are special factoring formulas, such as difference of squares?

**Tip:** Always check your factored expression by expanding it back out to ensure it matches the original polynomial.

Learn how to factor the polynomial 6xy² - 12x²y with a detailed step-by-step solution. This problem covers key algebraic concepts, including polynomials and factoring techniques. Suitable for students in Grades 9-12.

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