Math worksheet focusing on simplifying algebraic expressions using the distributive property and combining like terms.

To solve the given problems, we will use the distributive property and then combine like terms. Let's go through each expression step by step.

---

Expression 1: \( 6x - 2(x + 4) \)

1. Distribute \(-2\) across \((x + 4)\):
\[
6x - 2(x + 4) = 6x - 2x - 8
\]

2. Combine like terms:
\[
6x - 2x - 8 = 4x - 8
\]

Final Answer:
\[
\boxed{4x - 8}
\]

---

Expression 2: \( -9 + 2(1 - 3s) \)

1. Distribute \(2\) across \((1 - 3s)\):
\[
-9 + 2(1 - 3s) = -9 + 2 \cdot 1 - 2 \cdot 3s = -9 + 2 - 6s
\]

2. Combine like terms:
\[
-9 + 2 - 6s = -7 - 6s
\]

Final Answer:
\[
\boxed{-7 - 6s}
\]

---

Expression 3: \( 9(-6a + 3) - 4 \)

1. Distribute \(9\) across \((-6a + 3)\):
\[
9(-6a + 3) - 4 = 9 \cdot (-6a) + 9 \cdot 3 - 4 = -54a + 27 - 4
\]

2. Combine like terms:
\[
-54a + 27 - 4 = -54a + 23
\]

Final Answer:
\[
\boxed{-54a + 23}
\]

---

Expression 4: \( 3x + 3(1 + 8x) \)

1. Distribute \(3\) across \((1 + 8x)\):
\[
3x + 3(1 + 8x) = 3x + 3 \cdot 1 + 3 \cdot 8x = 3x + 3 + 24x
\]

2. Combine like terms:
\[
3x + 24x + 3 = 27x + 3
\]

Final Answer:
\[
\boxed{27x + 3}
\]

---

Expression 5: \( -(n + 2) - 2n \)

1. Distribute \(-1\) across \((n + 2)\):
\[
-(n + 2) - 2n = -n - 2 - 2n
\]

2. Combine like terms:
\[
-n - 2n - 2 = -3n - 2
\]

Final Answer:
\[
\boxed{-3n - 2}
\]

---

Expression 6: \( (s - 3)7.2 + 3s \)

1. Distribute \(7.2\) across \((s - 3)\):
\[
(s - 3)7.2 + 3s = 7.2s - 7.2 \cdot 3 + 3s = 7.2s - 21.6 + 3s
\]

2. Combine like terms:
\[
7.2s + 3s - 21.6 = 10.2s - 21.6
\]

Final Answer:
\[
\boxed{10.2s - 21.6}
\]

---

Expression 7: \( \frac{1}{2} + 3(2u + \frac{1}{2}) \)

1. Distribute \(3\) across \((2u + \frac{1}{2})\):
\[
\frac{1}{2} + 3(2u + \frac{1}{2}) = \frac{1}{2} + 3 \cdot 2u + 3 \cdot \frac{1}{2} = \frac{1}{2} + 6u + \frac{3}{2}
\]

2. Combine like terms:
\[
\frac{1}{2} + \frac{3}{2} + 6u = \frac{4}{2} + 6u = 2 + 6u
\]

Final Answer:
\[
\boxed{6u + 2}
\]

---

Expression 8: \( 2x + 3(x - 1) \)

1. Distribute \(3\) across \((x - 1)\):
\[
2x + 3(x - 1) = 2x + 3 \cdot x - 3 \cdot 1 = 2x + 3x - 3
\]

2. Combine like terms:
\[
2x + 3x - 3 = 5x - 3
\]

Final Answer:
\[
\boxed{5x - 3}
\]

---

Expression 9: \( -9(1 - 9a) + 7(2 + 9a) \)

1. Distribute \(-9\) across \((1 - 9a)\):
\[
-9(1 - 9a) = -9 \cdot 1 + (-9) \cdot (-9a) = -9 + 81a
\]

2. Distribute \(7\) across \((2 + 9a)\):
\[
7(2 + 9a) = 7 \cdot 2 + 7 \cdot 9a = 14 + 63a
\]

3. Combine the results:
\[
-9 + 81a + 14 + 63a
\]

4. Combine like terms:
\[
(-9 + 14) + (81a + 63a) = 5 + 144a
\]

Final Answer:
\[
\boxed{144a + 5}
\]

---

Expression 10: \( \frac{1}{2}(3x - 9) + 13x \)

1. Distribute \(\frac{1}{2}\) across \((3x - 9)\):
\[
\frac{1}{2}(3x - 9) = \frac{1}{2} \cdot 3x - \frac{1}{2} \cdot 9 = \frac{3}{2}x - \frac{9}{2}
\]

2. Combine with \(13x\):
\[
\frac{3}{2}x - \frac{9}{2} + 13x
\]

3. Express \(13x\) as a fraction with a common denominator:
\[
13x = \frac{26}{2}x
\]

4. Combine like terms:
\[
\frac{3}{2}x + \frac{26}{2}x - \frac{9}{2} = \frac{29}{2}x - \frac{9}{2}
\]

Final Answer:
\[
\boxed{\frac{29}{2}x - \frac{9}{2}}
\]

---

Expression 11: \( -(y + 3) + 8(1 - 6y) \)

1. Distribute \(-1\) across \((y + 3)\):
\[
-(y + 3) = -y - 3
\]

2. Distribute \(8\) across \((1 - 6y)\):
\[
8(1 - 6y) = 8 \cdot 1 + 8 \cdot (-6y) = 8 - 48y
\]

3. Combine the results:
\[
-y - 3 + 8 - 48y
\]

4. Combine like terms:
\[
(-y - 48y) + (-3 + 8) = -49y + 5
\]

Final Answer:
\[
\boxed{-49y + 5}
\]

---

Expression 12: \( -3(8x + 4) + \frac{1}{2}(6x - 24) \)

1. Distribute \(-3\) across \((8x + 4)\):
\[
-3(8x + 4) = -3 \cdot 8x + (-3) \cdot 4 = -24x - 12
\]

2. Distribute \(\frac{1}{2}\) across \((6x - 24)\):
\[
\frac{1}{2}(6x - 24) = \frac{1}{2} \cdot 6x + \frac{1}{2} \cdot (-24) = 3x - 12
\]

3. Combine the results:
\[
-24x - 12 + 3x - 12
\]

4. Combine like terms:
\[
(-24x + 3x) + (-12 - 12) = -21x - 24
\]

Final Answer:
\[
\boxed{-21x - 24}
\]

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Summary of Final Answers:

1. \( \boxed{4x - 8} \)
2. \( \boxed{-7 - 6s} \)
3. \( \boxed{-54a + 23} \)
4. \( \boxed{27x + 3} \)
5. \( \boxed{-3n - 2} \)
6. \( \boxed{10.2s - 21.6} \)
7. \( \boxed{6u + 2} \)
8. \( \boxed{5x - 3} \)
9. \( \boxed{144a + 5} \)
10. \( \boxed{\frac{29}{2}x - \frac{9}{2}} \)
11. \( \boxed{-49y + 5} \)
12. \( \boxed{-21x - 24} \)