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.