Sure, let's go through and simplify each expression step-by-step using the distributive property.
1. [tex]\(-5(-2f - 6)\)[/tex]
- Apply the distributive property:
[tex]\( -5 \cdot -2f + (-5 \cdot -6) = 10f + 30 \)[/tex]
2. [tex]\(8(1 + j)\)[/tex]
- Apply the distributive property:
[tex]\( 8 \cdot 1 + 8 \cdot j = 8 + 8j \)[/tex]
3. [tex]\(4(7 + 9)\)[/tex]
- Apply the distributive property:
[tex]\( 4 \cdot 7 + 4 \cdot 9 = 28 + 36 \)[/tex]
4. [tex]\(-3(-2g + 1)\)[/tex]
- Apply the distributive property:
[tex]\( -3 \cdot -2g + (-3 \cdot 1) = 6g - 3 \)[/tex]
5. [tex]\(-(1 - 6n)\)[/tex]
- Apply the distributive property:
[tex]\(-1 \cdot 1 + (-1 \cdot -6n) = -1 + 6n \)[/tex]
6. [tex]\((7 + 5c) \cdot 7\)[/tex]
- Apply the distributive property:
[tex]\( 7 \cdot 7 + 5c \cdot 7 = 49 + 35c \)[/tex]
7. [tex]\((-7 + w) \cdot 6\)[/tex]
- Apply the distributive property:
[tex]\( -7 \cdot 6 + w \cdot 6 = -42 + 6w \)[/tex]
8. [tex]\(-2(8 + 2q)\)[/tex]
- Apply the distributive property:
[tex]\( -2 \cdot 8 + (-2 \cdot 2q) = -16 - 4q \)[/tex]
9. [tex]\(-9(6 + k)\)[/tex]
- Apply the distributive property:
[tex]\( -9 \cdot 6 + (-9 \cdot k) = -54 - 9k \)[/tex]
10. [tex]\(-2(6g + 4)\)[/tex]
- Apply the distributive property:
[tex]\( -2 \cdot 6g + (-2 \cdot 4) = -12g - 8 \)[/tex]
11. [tex]\(-9(-7 - 7m)\)[/tex]
- Apply the distributive property:
[tex]\( -9 \cdot -7 + (-9 \cdot -7m) = 63 + 63m \)[/tex]
12. [tex]\((c - 6) \cdot 1\)[/tex]
- Apply the distributive property:
[tex]\( c \cdot 1 + (-6 \cdot 1) = c - 6 \)[/tex]
13. [tex]\((-6 + 9h) \cdot 6\)[/tex]
- Apply the distributive property:
[tex]\( -6 \cdot 6 + 9h \cdot 6 = -36 + 54h \)[/tex]
14. [tex]\(9(-3 - r)\)[/tex]
- Apply the distributive property:
[tex]\( 9 \cdot -3 + 9 \cdot -r = -27 - 9r \)[/tex]
15. [tex]\((2c + 6) \cdot -8\)[/tex]
- Apply the distributive property:
[tex]\( 2c \cdot -8 + 6 \cdot -8 = -16c - 48 \)[/tex]
16. [tex]\((1 - 8g) \cdot 2\)[/tex]
- Apply the distributive property:
[tex]\( 1 \cdot 2 + (-8g \cdot 2) = 2 - 16g \)[/tex]
17. [tex]\(9(-8p - 8)\)[/tex]
- Apply the distributive property:
[tex]\( 9 \cdot -8p + 9 \cdot -8 = -72p - 72 \)[/tex]
So, the simplified expressions are:
1. [tex]\( 10f + 30 \)[/tex]
2. [tex]\( 8 + 8j \)[/tex]
3. [tex]\( 28 + 36 \)[/tex]
4. [tex]\( 6g - 3 \)[/tex]
5. [tex]\( -1 + 6n \)[/tex]
6. [tex]\( 49 + 35c \)[/tex]
7. [tex]\( -42 + 6w \)[/tex]
8. [tex]\( -16 - 4q \)[/tex]
9. [tex]\( -54 - 9k \)[/tex]
10. [tex]\( -12g - 8 \)[/tex]
11. [tex]\( 63 + 63m \)[/tex]
12. [tex]\( c - 6 \)[/tex]
13. [tex]\( -36 + 54h \)[/tex]
14. [tex]\( -27 - 9r \)[/tex]
15. [tex]\( -16c - 48 \)[/tex]
16. [tex]\( 2 - 16g \)[/tex]
17. [tex]\( -72p - 72 \)[/tex]
