https://file.aiquickdraw.com/mathbot/file/1726122581200irlhjisp.jpg

Let's solve the polynomial expression provided in the image: \( 3x^3y - 27xy \).

### Step 1: Identify the greatest common factor (GCF).
Both terms share common factors. We can break each term down as follows:

1. \( 3x^3y = 3 \cdot x^3 \cdot y \)
2. \( 27xy = 27 \cdot x \cdot y \)

The greatest common factor (GCF) is:
\[
3xy
\]

### Step 2: Factor out the GCF.
Now, we factor out \( 3xy \) from both terms:
\[
3x^3y - 27xy = 3xy(x^2 - 9)
\]

### Step 3: Factor further if possible.
The expression \( x^2 - 9 \) is a difference of squares:
\[
x^2 - 9 = (x - 3)(x + 3)
\]

### Final factored form:
\[
3x^3y - 27xy = 3xy(x - 3)(x + 3)
\]

Thus, the correct answer is:
\[
3x^3y - 27xy = 3xy(x - 3)(x + 3)
\]

Let me know if you would like more details or if you have any questions!

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### Related Questions:
1. How do you identify the greatest common factor of a polynomial?
2. What is the difference of squares and how is it factored?
3. Can all polynomials be factored? Why or why not?
4. What are the steps to factoring a trinomial?
5. How does factoring help in solving polynomial equations?

### Tip:
Always check if the terms inside the parentheses can be factored further after factoring out the GCF!

Factor completely, or state that the polynomial is prime: 3x^3y - 27xy.

Learn how to factor the polynomial 3x^3y - 27xy completely. This solution demonstrates how to identify the greatest common factor (GCF) and apply the difference of squares. Suitable for high school students in Grades 9-12.

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