Kuta Software Algebra 1 worksheet featuring 12 exercises on simplifying expressions using the distributive property, complete with answer keys.

The task involves simplifying expressions using the distributive property. The distributive property states that for any numbers \( a \), \( b \), and \( c \):

\[
a(b + c) = ab + ac
\]

This means we multiply the term outside the parentheses by each term inside the parentheses.

Let's solve each problem step by step:

---

Problem 1: Simplify \(-6(a + 8)\)

1. Distribute \(-6\) to both \(a\) and \(8\):
\[
-6(a + 8) = (-6 \cdot a) + (-6 \cdot 8)
\]
2. Perform the multiplications:
\[
-6 \cdot a = -6a \quad \text{and} \quad -6 \cdot 8 = -48
\]
3. Combine the results:
\[
-6a - 48
\]

Answer:
\[
\boxed{-6a - 48}
\]

---

Problem 2: Simplify \(4(1 + 9x)\)

1. Distribute \(4\) to both \(1\) and \(9x\):
\[
4(1 + 9x) = (4 \cdot 1) + (4 \cdot 9x)
\]
2. Perform the multiplications:
\[
4 \cdot 1 = 4 \quad \text{and} \quad 4 \cdot 9x = 36x
\]
3. Combine the results:
\[
4 + 36x
\]

Answer:
\[
\boxed{4 + 36x}
\]

---

Problem 3: Simplify \(6(-5n + 7)\)

1. Distribute \(6\) to both \(-5n\) and \(7\):
\[
6(-5n + 7) = (6 \cdot -5n) + (6 \cdot 7)
\]
2. Perform the multiplications:
\[
6 \cdot -5n = -30n \quad \text{and} \quad 6 \cdot 7 = 42
\]
3. Combine the results:
\[
-30n + 42
\]

Answer:
\[
\boxed{-30n + 42}
\]

---

Problem 4: Simplify \((9m + 10) \cdot 2\)

1. Distribute \(2\) to both \(9m\) and \(10\):
\[
(9m + 10) \cdot 2 = (2 \cdot 9m) + (2 \cdot 10)
\]
2. Perform the multiplications:
\[
2 \cdot 9m = 18m \quad \text{and} \quad 2 \cdot 10 = 20
\]
3. Combine the results:
\[
18m + 20
\]

Answer:
\[
\boxed{18m + 20}
\]

---

Problem 5: Simplify \((-4 - 3n) \cdot -8\)

1. Distribute \(-8\) to both \(-4\) and \(-3n\):
\[
(-4 - 3n) \cdot -8 = (-8 \cdot -4) + (-8 \cdot -3n)
\]
2. Perform the multiplications:
\[
-8 \cdot -4 = 32 \quad \text{and} \quad -8 \cdot -3n = 24n
\]
3. Combine the results:
\[
32 + 24n
\]

Answer:
\[
\boxed{32 + 24n}
\]

---

Problem 6: Simplify \(8(-b - 4)\)

1. Distribute \(8\) to both \(-b\) and \(-4\):
\[
8(-b - 4) = (8 \cdot -b) + (8 \cdot -4)
\]
2. Perform the multiplications:
\[
8 \cdot -b = -8b \quad \text{and} \quad 8 \cdot -4 = -32
\]
3. Combine the results:
\[
-8b - 32
\]

Answer:
\[
\boxed{-8b - 32}
\]

---

Problem 7: Simplify \((1 - 7n) \cdot 5\)

1. Distribute \(5\) to both \(1\) and \(-7n\):
\[
(1 - 7n) \cdot 5 = (5 \cdot 1) + (5 \cdot -7n)
\]
2. Perform the multiplications:
\[
5 \cdot 1 = 5 \quad \text{and} \quad 5 \cdot -7n = -35n
\]
3. Combine the results:
\[
5 - 35n
\]

Answer:
\[
\boxed{5 - 35n}
\]

---

Problem 8: Simplify \(-6(x + 4)\)

1. Distribute \(-6\) to both \(x\) and \(4\):
\[
-6(x + 4) = (-6 \cdot x) + (-6 \cdot 4)
\]
2. Perform the multiplications:
\[
-6 \cdot x = -6x \quad \text{and} \quad -6 \cdot 4 = -24
\]
3. Combine the results:
\[
-6x - 24
\]

Answer:
\[
\boxed{-6x - 24}
\]

---

Problem 9: Simplify \(5(3m - 6)\)

1. Distribute \(5\) to both \(3m\) and \(-6\):
\[
5(3m - 6) = (5 \cdot 3m) + (5 \cdot -6)
\]
2. Perform the multiplications:
\[
5 \cdot 3m = 15m \quad \text{and} \quad 5 \cdot -6 = -30
\]
3. Combine the results:
\[
15m - 30
\]

Answer:
\[
\boxed{15m - 30}
\]

---

Problem 10: Simplify \((-6p + 7) \cdot -4\)

1. Distribute \(-4\) to both \(-6p\) and \(7\):
\[
(-6p + 7) \cdot -4 = (-4 \cdot -6p) + (-4 \cdot 7)
\]
2. Perform the multiplications:
\[
-4 \cdot -6p = 24p \quad \text{and} \quad -4 \cdot 7 = -28
\]
3. Combine the results:
\[
24p - 28
\]

Answer:
\[
\boxed{24p - 28}
\]

---

Problem 11: Simplify \(5(b - 1)\)

1. Distribute \(5\) to both \(b\) and \(-1\):
\[
5(b - 1) = (5 \cdot b) + (5 \cdot -1)
\]
2. Perform the multiplications:
\[
5 \cdot b = 5b \quad \text{and} \quad 5 \cdot -1 = -5
\]
3. Combine the results:
\[
5b - 5
\]

Answer:
\[
\boxed{5b - 5}
\]

---

Problem 12: Simplify \((x + 9) \cdot 5\)

1. Distribute \(5\) to both \(x\) and \(9\):
\[
(x + 9) \cdot 5 = (5 \cdot x) + (5 \cdot 9)
\]
2. Perform the multiplications:
\[
5 \cdot x = 5x \quad \text{and} \quad 5 \cdot 9 = 45
\]
3. Combine the results:
\[
5x + 45
\]

Answer:
\[
\boxed{5x + 45}
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1) & \ -6a - 48 \\
2) & \ 4 + 36x \\
3) & \ -30n + 42 \\
4) & \ 18m + 20 \\
5) & \ 32 + 24n \\
6) & \ -8b - 32 \\
7) & \ 5 - 35n \\
8) & \ -6x - 24 \\
9) & \ 15m - 30 \\
10) & \ 24p - 28 \\
11) & \ 5b - 5 \\
12) & \ 5x + 45
\end{aligned}
}
\]