To factor the expression \( 6xy^2 - 12x^2y \) given that it's equal to \( 6xy \), let's follow these steps:

### 1. Factor out the common terms:
We start by identifying the greatest common factor (GCF) in the expression \( 6xy^2 - 12x^2y \).

- The GCF of the coefficients 6 and 12 is 6.
- The GCF of the variables \(x\) and \(x^2\) is \(x\).
- The GCF of the variables \(y^2\) and \(y\) is \(y\).

So, the GCF of the entire expression is \( 6xy \).

### 2. Factor the expression:
We can factor out \( 6xy \) from each term in the expression:

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

### 3. Set it equal to \( 6xy \):
Since the original equation is \( 6xy^2 - 12x^2y = 6xy \), we substitute the factored form into the equation:

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

### 4. Simplify the equation:
Now, divide both sides of the equation by \( 6xy \), assuming \( 6xy \neq 0 \):

\[
y - 2x = 1
\]

Thus, the factored form leads to the equation \( y - 2x = 1 \).

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions you might explore next:
1. How do you factor polynomials with three or more terms?
2. What is the process for factoring quadratics?
3. How do you factor expressions involving higher powers, like cubes?
4. How do you solve equations after factoring them?
5. How do you determine when an expression is prime and cannot be factored further?

**Tip:** Always double-check the common factors in both the coefficients and the variables when factoring expressions.

Learn how to factor the expression 6xy² - 12x²y = 6xy step-by-step. Understand the process of factoring polynomials involving common terms and variables. Suitable for high school students studying algebra and polynomial equations.

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