https://file.aiquickdraw.com/mathbot/file/1729792567273i4x7rhrz.jpg

Let's work through the factoring of each polynomial expression shown in the image:

1. \( y^2 - 25 \)
   This is a difference of squares:
   \[
   y^2 - 25 = (y - 5)(y + 5)
   \]

2. \( y^2 - 6y + 9 \)
   This is a perfect square trinomial:
   \[
   y^2 - 6y + 9 = (y - 3)(y - 3) = (y - 3)^2
   \]

3. \( 9y^2 - 16 \)
   This is another difference of squares:
   \[
   9y^2 - 16 = (3y - 4)(3y + 4)
   \]

4. \( 4y^2 + 12y + 9 \)
   This is also a perfect square trinomial:
   \[
   4y^2 + 12y + 9 = (2y + 3)(2y + 3) = (2y + 3)^2
   \]

Would you like more details or have any questions about these factorizations?

Here are five related questions to expand on these concepts:
1. How do you recognize a difference of squares when factoring?
2. What steps can be taken to factor non-perfect square trinomials?
3. What is the general form of a perfect square trinomial?
4. Can you factor a polynomial that is not a difference of squares or perfect square trinomial?
5. How does the distributive property (FOIL method) verify factorizations?

**Tip:** Always check for the greatest common factor (GCF) before attempting to factor polynomials. This simplifies the factoring process.

Rewrite each of the following polynomial expressions in factored form:
1. y^2 - 25
2. y^2 - 6y + 9
3. 9y^2 - 16
4. 4y^2 + 12y + 9

Learn how to factor quadratic polynomial expressions like y^2 - 25 and y^2 - 6y + 9. This problem explores the difference of squares and perfect square trinomials, covering core algebraic concepts for students in Grades 8-10.

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