Find the greatest common factor of the following list of terms.

x cubed yx3y​, 

x squared yx2y​, 

and xyxy

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Part 1

The greatest common factor is 

To find the greatest common factor (GCF) of the given terms, we need to determine the highest power of each variable that is common across all terms.

Given terms:
1. \( x^3y \)
2. \( x^2y \)
3. \( xy \)

**Step 1: Identify the factors in each term:**

- \( x^3y \) has factors \( x^3 \) and \( y \).
- \( x^2y \) has factors \( x^2 \) and \( y \).
- \( xy \) has factors \( x \) and \( y \).

**Step 2: Determine the smallest power of each variable common to all terms:**

- For \( x \): The smallest power of \( x \) across the terms is \( x^1 \).
- For \( y \): The power of \( y \) is \( y^1 \) in all terms.

**Step 3: Multiply these factors together to find the GCF:**

The greatest common factor is the product of these minimum powers:
\[
\text{GCF} = x^1 \cdot y^1 = xy
\]

So, the greatest common factor is **\( xy \)**.

Would you like any further details on this solution? Here are five related questions that might help you explore the topic further:

1. How do you find the greatest common factor of polynomials with more than two terms?
2. What is the process of factoring out the greatest common factor from a polynomial?
3. How can the concept of GCF be extended to multiple variables and more complex expressions?
4. How does the GCF relate to simplifying algebraic fractions?
5. How can you apply the concept of GCF to solve real-world problems involving algebraic expressions?

**Tip:** When finding the GCF of algebraic terms, always look for the lowest power of each variable that appears in all terms.

Learn how to find the greatest common factor (GCF) of x^3y, x^2y, and xy with a detailed step-by-step solution. This problem covers algebraic concepts such as polynomials and GCF. Suitable for students in Grades 7-9.

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