Factor the greatest common factor​ (GCF) from the following polynomial.
7 x squared y minus 21 x cubed y squared


To factor the greatest common factor (GCF) from the polynomial \(7x^2y - 21x^3y^2\), follow these steps:

1. **Identify the GCF of the coefficients**:  
   The coefficients are 7 and 21. The GCF of 7 and 21 is 7.

2. **Identify the GCF of the variable terms**:  
   - For \(x^2\) and \(x^3\), the GCF is \(x^2\).
   - For \(y\) and \(y^2\), the GCF is \(y\).

3. **Combine the GCF of the coefficients and variable terms**:  
   The overall GCF is \(7x^2y\).

4. **Factor the GCF out of the polynomial**:  
   \[
   7x^2y - 21x^3y^2 = 7x^2y(1 - 3xy)
   \]

So, the factored form of the polynomial is:
\[
7x^2y(1 - 3xy)
\]

Would you like more details or have any questions about this process? 

Here are five related questions for further practice:
1. What is the GCF of \(12x^4y^2\) and \(18x^3y^3\)?
2. How do you factor the polynomial \(10x^3 - 5x^2\)?
3. What is the result of factoring \(15xy^2 - 9x^2y\)?
4. What is the GCF of \(24x^5y^3\) and \(16x^3y^4\)?
5. How would you factor \(6x^3y^2 - 9x^2y^3 + 3xy^4\)?

**Tip:** Always start by finding the GCF of both the coefficients and the variables separately, then combine them to factor the polynomial.

Learn how to factor the greatest common factor (GCF) from the polynomial 7x^2y - 21x^3y^2 with a detailed step-by-step solution. This problem involves polynomials and GCF factoring, suitable for students in Grades 7-9.

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