The expression you've provided is:

\[
x^2 + 3xy - 18y^2
\]

If you're looking to factor it, we can approach this by grouping terms and looking for patterns. Here's the process:

1. First, check if there's a common factor in all terms. In this case, there isn't.
2. Next, try factoring by grouping or applying other factoring techniques like trial and error, if the expression fits a recognizable form.

The expression doesn't easily fit into a standard factoring technique, but we can attempt factoring by trial.

The expression can be factored as:

\[
(x + 6y)(x - 3y)
\]

Thus, the factored form of \( x^2 + 3xy - 18y^2 \) is:

\[
(x + 6y)(x - 3y)
\]

Would you like more details or clarification on any steps?

Here are 5 related questions to expand your understanding:
1. How do you factor a trinomial using trial and error?
2. Can the distributive property help in simplifying complex expressions?
3. What are the steps to check if a factorization is correct?
4. How can factoring be applied to solve quadratic equations?
5. What are the key differences between factoring and expanding polynomials?

**Tip:** Always recheck factorizations by multiplying the factors to verify the original expression.

Discover how to factor the polynomial expression x^2 + 3xy - 18y^2 using factoring techniques such as trial and error. This step-by-step guide covers key algebraic concepts, making it perfect for students in Grades 9-11.

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