Algebra math workbook with 100 worksheets focusing on simple distribution problems.

Problem Analysis:

The image shows a section from a math workbook focusing on simple distribution problems in algebra. The tasks are divided into two parts:
1. Multiply: Distribute the given coefficients across the terms inside the parentheses.
2. Factor: Factor out the greatest common factor (GCF) from the expressions.

Let's solve each part step by step.

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Part 1: Multiply

#### Step-by-Step Solutions for Multiplication Problems

1. \(-9(5x + 6)\)
- Distribute \(-9\) to both \(5x\) and \(6\):
\[
-9(5x) + (-9)(6) = -45x - 54
\]
- Answer: \(-45x - 54\)

2. \(2(2x + 4)\)
- Distribute \(2\) to both \(2x\) and \(4\):
\[
2(2x) + 2(4) = 4x + 8
\]
- Answer: \(4x + 8\)

3. \(2(8x - 6)\)
- Distribute \(2\) to both \(8x\) and \(-6\):
\[
2(8x) + 2(-6) = 16x - 12
\]
- Answer: \(16x - 12\)

4. \(-9(-7x - 6)\)
- Distribute \(-9\) to both \(-7x\) and \(-6\):
\[
-9(-7x) + (-9)(-6) = 63x + 54
\]
- Answer: \(63x + 54\)

5. \(-6(6x + 7)\)
- Distribute \(-6\) to both \(6x\) and \(7\):
\[
-6(6x) + (-6)(7) = -36x - 42
\]
- Answer: \(-36x - 42\)

6. \(-2(-9x + 4)\)
- Distribute \(-2\) to both \(-9x\) and \(4\):
\[
-2(-9x) + (-2)(4) = 18x - 8
\]
- Answer: \(18x - 8\)

7. \(-7(-6x + 2)\)
- Distribute \(-7\) to both \(-6x\) and \(2\):
\[
-7(-6x) + (-7)(2) = 42x - 14
\]
- Answer: \(42x - 14\)

8. \(-8(-8x + 3)\)
- Distribute \(-8\) to both \(-8x\) and \(3\):
\[
-8(-8x) + (-8)(3) = 64x - 24
\]
- Answer: \(64x - 24\)

9. \(2(3x - 7)\)
- Distribute \(2\) to both \(3x\) and \(-7\):
\[
2(3x) + 2(-7) = 6x - 14
\]
- Answer: \(6x - 14\)

10. \(-4(-9x - 2)\)
- Distribute \(-4\) to both \(-9x\) and \(-2\):
\[
-4(-9x) + (-4)(-2) = 36x + 8
\]
- Answer: \(36x + 8\)

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Part 2: Factor

#### Step-by-Step Solutions for Factoring Problems

1. \(24x - 48\)
- Identify the GCF of \(24x\) and \(48\), which is \(24\).
- Factor out \(24\):
\[
24x - 48 = 24(x - 2)
\]
- Answer: \(24(x - 2)\)

2. \(10x - 25\)
- Identify the GCF of \(10x\) and \(25\), which is \(5\).
- Factor out \(5\):
\[
10x - 25 = 5(2x - 5)
\]
- Answer: \(5(2x - 5)\)

3. \(24x + 32\)
- Identify the GCF of \(24x\) and \(32\), which is \(8\).
- Factor out \(8\):
\[
24x + 32 = 8(3x + 4)
\]
- Answer: \(8(3x + 4)\)

4. \(-16x + 48\)
- Identify the GCF of \(-16x\) and \(48\), which is \(-16\).
- Factor out \(-16\):
\[
-16x + 48 = -16(x - 3)
\]
- Answer: \(-16(x - 3)\)

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Final Answers:

#### Multiply
1. \(-45x - 54\)
2. \(4x + 8\)
3. \(16x - 12\)
4. \(63x + 54\)
5. \(-36x - 42\)
6. \(18x - 8\)
7. \(42x - 14\)
8. \(64x - 24\)
9. \(6x - 14\)
10. \(36x + 8\)

#### Factor
1. \(24(x - 2)\)
2. \(5(2x - 5)\)
3. \(8(3x + 4)\)
4. \(-16(x - 3)\)

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Multiply:} & \text{Factor:} \\
1. \, -45x - 54 & 1. \, 24(x - 2) \\
2. \, 4x + 8 & 2. \, 5(2x - 5) \\
3. \, 16x - 12 & 3. \, 8(3x + 4) \\
4. \, 63x + 54 & 4. \, -16(x - 3) \\
5. \, -36x - 42 & \\
6. \, 18x - 8 & \\
7. \, 42x - 14 & \\
8. \, 64x - 24 & \\
9. \, 6x - 14 & \\
10. \, 36x + 8 &
\end{array}
}
\]