To find the Greatest Common Factor (GCF) of the terms \(9x^3y^3\), \(6x^4y^3\), and \(2x^5y^2\), follow these steps:

1. **Find the GCF of the coefficients (numerical parts):**
   - Coefficients: 9, 6, and 2.
   - The GCF of 9, 6, and 2 is 1, as 1 is the largest number that divides all three.

2. **Find the GCF of the \(x\) terms:**
   - For \(x^3\), \(x^4\), and \(x^5\), the lowest exponent is 3.
   - So, the GCF of the \(x\) terms is \(x^3\).

3. **Find the GCF of the \(y\) terms:**
   - For \(y^3\), \(y^3\), and \(y^2\), the lowest exponent is 2.
   - So, the GCF of the \(y\) terms is \(y^2\).

Therefore, the GCF of \(9x^3y^3\), \(6x^4y^3\), and \(2x^5y^2\) is:

\[
\text{GCF} = 1 \cdot x^3 \cdot y^2 = x^3y^2
\]

Would you like further details or have any questions?

Here are 8 related questions:
1. How do you find the GCF of multiple algebraic expressions?
2. What is the GCF of \(12x^4y\) and \(18x^2y^3\)?
3. How can you factor out the GCF from a polynomial?
4. What is the role of exponents in determining the GCF of variables?
5. What if the coefficients were fractions? How would you find the GCF?
6. Can you find the LCM (Least Common Multiple) of \(9x^3y^3\) and \(6x^4y^3\)?
7. What is the difference between GCF and LCM in algebraic terms?
8. How would you factor \(12x^3y^2 + 6x^4y^3 + 3x^5y\) using the GCF?

**Tip:** When factoring polynomials, always start by finding the GCF of all the terms to simplify the expression.

Learn how to find the Greatest Common Factor (GCF) of the algebraic terms 9x^3y^3, 6x^4y^3, and 2x^5y^2. Follow a step-by-step solution methodically explaining the process of identifying and computing the GCF. Suitable for middle school students (Grades 6-8) learning about polynomials and exponents in algebra.

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