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Let's work through each polynomial and factor them.

1. \( w^2 - 9 \)  
   This is a difference of squares. It can be factored as:
   \[
   w^2 - 9 = (w - 3)(w + 3)
   \]

2. \( w^2 - 6w + 9 \)  
   This is a perfect square trinomial, and can be factored as:
   \[
   w^2 - 6w + 9 = (w - 3)(w - 3) = (w - 3)^2
   \]

3. \( 9w^2 - 25 \)  
   Another difference of squares. It can be factored as:
   \[
   9w^2 - 25 = (3w - 5)(3w + 5)
   \]

4. \( 4w^2 + 12w + 9 \)  
   This is also a perfect square trinomial. It can be factored as:
   \[
   4w^2 + 12w + 9 = (2w + 3)(2w + 3) = (2w + 3)^2
   \]

Would you like more details on any of these? 

Here are some related questions you might find helpful:
1. How do you recognize a difference of squares?
2. What makes a trinomial a perfect square?
3. How do you factor polynomials with a greatest common factor (GCF)?
4. Can every quadratic equation be factored?
5. What are some methods to solve quadratics if factoring isn't possible?

**Tip:** Always check if you can factor out a greatest common factor before using other factoring techniques!

Rewrite each of the following polynomial expressions in factored form: w^2 - 9, w^2 - 6w + 9, 9w^2 - 25, 4w^2 + 12w + 9.

Learn how to factor polynomial expressions such as w^2 - 9, w^2 - 6w + 9, 9w^2 - 25, and 4w^2 + 12w + 9. This lesson covers the difference of squares and perfect square trinomials, providing step-by-step solutions for students in Grades 9-10.

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