This image displays the answer key for the 'Factoring Expressions (A)' worksheet, showing the correct factored forms for 30 different algebraic equations.

The task involves factoring each given algebraic expression. Factoring is the process of rewriting an expression as a product of its factors. Here's a detailed explanation of how to factor each type of expression:

General Steps for Factoring:

1. Identify the Greatest Common Factor (GCF): Look for the largest number and variable that divides all terms in the expression.
2. Factor out the GCF: Divide each term by the GCF and write the expression as a product of the GCF and the remaining terms.
3. Check the result: Ensure that when you distribute the GCF back, you get the original expression.

Detailed Solutions:

#### Section 1: Expressions with One Variable
1. 9a - 18
- GCF: 9
- Factor: \( 9(a - 2) \)

2. 4a² - 16a
- GCF: 4a
- Factor: \( 4a(a - 4) \)

3. 6b² + 12b
- GCF: 6b
- Factor: \( 6b(b + 2) \)

4. 9b² + 27b
- GCF: 9b
- Factor: \( 9b(b + 3) \)

5. 3b + 12
- GCF: 3
- Factor: \( 3(b + 4) \)

6. 4x² - 20x
- GCF: 4x
- Factor: \( 4x(x - 5) \)

7. 7c² + 56c
- GCF: 7c
- Factor: \( 7c(c + 8) \)

8. b² + b
- GCF: b
- Factor: \( b(b + 1) \)

9. 8b - 48
- GCF: 8
- Factor: \( 8(b - 6) \)

10. 4x + 36
- GCF: 4
- Factor: \( 4(x + 9) \)

#### Section 2: Expressions with Two Variables
11. 2b² - 12b
- GCF: 2b
- Factor: \( 2b(b - 6) \)

12. 2b² + 18b
- GCF: 2b
- Factor: \( 2b(b + 9) \)

13. 6c - 30
- GCF: 6
- Factor: \( 6(c - 5) \)

14. 8b² + 32b
- GCF: 8b
- Factor: \( 8b(b + 4) \)

15. 6b² - 6b
- GCF: 6b
- Factor: \( 6b(b - 1) \)

16. 2a - 12
- GCF: 2
- Factor: \( 2(a - 6) \)

17. 6a² + 48a
- GCF: 6a
- Factor: \( 6a(a + 8) \)

18. 8x - 32
- GCF: 8
- Factor: \( 8(x - 4) \)

19. 8a² - 72a
- GCF: 8a
- Factor: \( 8a(a - 9) \)

20. a² - 2a
- GCF: a
- Factor: \( a(a - 2) \)

#### Section 3: More Complex Expressions
21. 4y + 20
- GCF: 4
- Factor: \( 4(y + 5) \)

22. 7b + 49
- GCF: 7
- Factor: \( 7(b + 7) \)

23. a² + 5a
- GCF: a
- Factor: \( a(a + 5) \)

24. 9z - 72
- GCF: 9
- Factor: \( 9(z - 8) \)

25. 4c + 4
- GCF: 4
- Factor: \( 4(c + 1) \)

26. 6a + 42
- GCF: 6
- Factor: \( 6(a + 7) \)

27. 9b² + 9b
- GCF: 9b
- Factor: \( 9b(b + 1) \)

28. 5a - 30
- GCF: 5
- Factor: \( 5(a - 6) \)

29. 3a² + 27a
- GCF: 3a
- Factor: \( 3a(a + 9) \)

30. c² - 5c
- GCF: c
- Factor: \( c(c - 5) \)

Final Answer:

\[
\boxed{
\begin{array}{lll}
1. & 9(a - 2) & 11. & 2b(b - 6) & 21. & 4(y + 5) \\
2. & 4a(a - 4) & 12. & 2b(b + 9) & 22. & 7(b + 7) \\
3. & 6b(b + 2) & 13. & 6(c - 5) & 23. & a(a + 5) \\
4. & 9b(b + 3) & 14. & 8b(b + 4) & 24. & 9(z - 8) \\
5. & 3(b + 4) & 15. & 6b(b - 1) & 25. & 4(c + 1) \\
6. & 4x(x - 5) & 16. & 2(a - 6) & 26. & 6(a + 7) \\
7. & 7c(c + 8) & 17. & 6a(a + 8) & 27. & 9b(b + 1) \\
8. & b(b + 1) & 18. & 8(x - 4) & 28. & 5(a - 6) \\
9. & 8(b - 6) & 19. & 8a(a - 9) & 29. & 3a(a + 9) \\
10. & 4(x + 9) & 20. & a(a - 2) & 30. & c(c - 5) \\
\end{array}
}
\]