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The image contains a list of quadratic expressions that need to be factored. Let's go through each expression and factor them completely:

1. **a**. \( x^2 - 9x \)
   - Factor out \( x \):
   - \( x(x - 9) \)

2. **b**. \( 2x^2 + 7x \)
   - Factor out the greatest common factor (GCF):
   - \( x(2x + 7) \)

3. **c**. \( 4x^2 - 10x \)
   - Factor out the GCF:
   - \( 2x(2x - 5) \)

4. **d**. \( 6x^2 - 15x \)
   - Factor out the GCF:
   - \( 3x(2x - 5) \)

5. **e**. \( 9x^2 - 25 \)
   - This is a difference of squares:
   - \( (3x - 5)(3x + 5) \)

6. **f**. \( x^2 - 1 \)
   - This is a difference of squares:
   - \( (x - 1)(x + 1) \)

7. **g**. \( x^2 - 9 \)
   - This is a difference of squares:
   - \( (x - 3)(x + 3) \)

8. **h**. \( 9x^2 - 9 \)
   - Factor out the GCF:
   - \( 9(x^2 - 1) \)
   - Then factor the difference of squares:
   - \( 9(x - 1)(x + 1) \)

9. **i**. \( 4x^2 - 9 \)
   - This is a difference of squares:
   - \( (2x - 3)(2x + 3) \)

10. **j**. \( x^2 - 8x + 16 \)
    - This is a perfect square trinomial:
    - \( (x - 4)^2 \)

11. **k**. \( 2x^2 - 10x + 25 \)
    - Factor out the GCF:
    - \( 2(x^2 - 5x + \frac{25}{2}) \)
    - \( x^2 - 5x + 6.25 \) is not easily factorizable with integer coefficients, so this would remain as:
    - \( 2(x - \frac{5}{2})^2 \)

12. **l**. \( 2x^2 + 8x + 8 \)
    - Factor out the GCF:
    - \( 2(x^2 + 4x + 4) \)
    - \( x^2 + 4x + 4 \) is a perfect square trinomial:
    - \( 2(x + 2)^2 \)

13. **m**. \( 16x^2 + 40x + 25 \)
    - This is a perfect square trinomial:
    - \( (4x + 5)^2 \)

14. **n**. \( 9x^2 + 12x + 4 \)
    - This is a perfect square trinomial:
    - \( (3x + 2)^2 \)

15. **o**. \( x^2 - 22x + 121 \)
    - This is a perfect square trinomial:
    - \( (x - 11)^2 \)

Would you like a more detailed explanation for any of these factorizations? 

Here are five related questions that expand on this topic:
1. How do you identify a perfect square trinomial?
2. What are the steps to factor a quadratic expression?
3. How can you factor a difference of squares?
4. How do you determine the greatest common factor in an expression?
5. What do you do when a quadratic cannot be factored easily using integer coefficients?

**Tip:** When factoring, always check if there is a greatest common factor (GCF) before attempting other factoring methods.

Fully factorize the following quadratic expressions.

Learn how to fully factorize various quadratic expressions including difference of squares, perfect square trinomials, and using the greatest common factor (GCF). This tutorial is perfect for students in Grades 8-10 and covers key algebraic concepts.

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