Let's work through the factoring problems step by step from the image:

1. $y^2 + 6y + 9$

This is a perfect square trinomial: $y^2 + 6y + 9 = (y + 3)^2$

2. $y^2 + 22y + 121$

This is also a perfect square trinomial: $y^2 + 22y + 121 = (y + 11)^2$

3. $y^2 - 14y + 49$

Another perfect square trinomial: $y^2 - 14y + 49 = (y - 7)^2$

4. $y^2 + 26y + 169$

Perfect square trinomial: $y^2 + 26y + 169 = (y + 13)^2$

5. $y^2 - 121$

This is a difference of squares: $y^2 - 121 = (y - 11)(y + 11)$

6. $y^2 - 256$

Difference of squares: $y^2 - 256 = (y - 16)(y + 16)$

7. $y^2 - 64$

Difference of squares: $y^2 - 64 = (y - 8)(y + 8)$

8. $y^3 - 1$

This is a difference of cubes: $y^3 - 1 = (y - 1)(y^2 + y + 1)$

9. $y^3 + 216$

Sum of cubes: $y^3 + 216 = (y + 6)(y^2 - 6y + 36)$

10. $y^3 - 729$

Difference of cubes: $y^3 - 729 = (y - 9)(y^2 + 9y + 81)$

Would you like more details on any of these factorizations, or do you have specific questions?

Here are five related questions for further exploration:

1. What is the process for identifying a perfect square trinomial?
2. How do you factor the sum or difference of cubes?
3. What is the significance of recognizing patterns like the difference of squares?
4. Can the quadratic formula help in factoring non-special products?
5. How can completing the square aid in factoring?

Tip: When factoring polynomials, always check if the expression fits common patterns like perfect squares, sum/difference of cubes, or difference of squares first.