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Let's go through each expression and factorize them step-by-step. I’ll provide detailed solutions for each.

1. **\( a^2 + 6a + 8 \)**
   - **Solution**: Factor as \( (a+2)(a+4) \).

2. **\( m^2 + 9m + 18 \)**
   - **Solution**: Factor as \( (m+3)(m+6) \).

3. **\( y^2 + 13y + 42 \)**
   - **Solution**: Factor as \( (y+6)(y+7) \).

4. **\( p^2 + 7p + 12 \)**
   - **Solution**: Factor as \( (p+3)(p+4) \).

5. **\( x^2 + 12x + 20 \)**
   - **Solution**: Factor as \( (x+10)(x+2) \).

6. **\( u^2 + 17n + 42 \)** 
   - It appears there may be a typo here with the variable mismatch. Assuming it is **\( n^2 + 17n + 42 \)**:
   - **Solution**: Factor as \( (n+3)(n+14) \).

7. **\( s^2 + 21s + 54 \)**
   - **Solution**: Factor as \( (s+3)(s+18) \).

8. **\( a^2 + 18a + 56 \)**
   - **Solution**: Factor as \( (a+4)(a+14) \).

9. **\( x^2 - 3x - 4 \)**
   - **Solution**: Factor as \( (x-4)(x+1) \).

10. **\( a^2 - 2a - 8 \)**
    - **Solution**: Factor as \( (a-4)(a+2) \).

11. **\( p^2 - 5p - 24 \)**
    - **Solution**: Factor as \( (p-8)(p+3) \).

12. **\( y^2 + y - 6 \)**
    - **Solution**: Factor as \( (y+3)(y-2) \).

13. **\( x^2 + 7x - 8 \)**
    - **Solution**: Factor as \( (x-1)(x+8) \).

14. **\( q^2 + 5q - 24 \)**
    - **Solution**: Factor as \( (q+8)(q-3) \).

15. **\( m^2 + 12m - 45 \)**
    - **Solution**: Factor as \( (m+15)(m-3) \).

16. **\( a^2 + 18a - 63 \)**
    - **Solution**: Factor as \( (a-3)(a+21) \).

17. **\( y^2 - 2x + 1 \)**
    - **Solution**: Factor as \(

This guide provides step-by-step solutions for factorizing quadratic expressions like a^2 + 6a + 8 and m^2 + 9m + 18. Suitable for Grades 7-9, it covers key algebra concepts including the factoring of quadratic expressions and the methods involved in breaking down expressions of the form ax^2 + bx + c.

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