It looks like you've uploaded a page from an algebra workbook titled
"Simple Distribution Problems", which includes two types of problems:
1.
Multiply – Distributing a number across terms inside parentheses.
2.
Factor – Factoring out the greatest common factor (GCF) from expressions.
Let’s go through each problem and verify or explain the solution step by step.
---
🔹 Part 1: Multiply (Distributive Property)
We apply the distributive property:
> $ a(b + c) = ab + ac $
#### 1. $-9(5x + 6)$
$$
-9 \cdot 5x = -45x,\quad -9 \cdot 6 = -54
\Rightarrow -45x - 54 \quad \text{
✔ Correct}
$$
#### 2. $2(2x + 4)$
$$
2 \cdot 2x = 4x,\quad 2 \cdot 4 = 8
\Rightarrow 4x + 8 \quad \text{
✔ Correct}
$$
#### 3. $2(8x - 6)$
$$
2 \cdot 8x = 16x,\quad 2 \cdot (-6) = -12
\Rightarrow 16x - 12 \quad \text{
✔ Correct}
$$
#### 4. $-9(-7x - 6)$
$$
-9 \cdot (-7x) = 63x,\quad -9 \cdot (-6) = 54
\Rightarrow 63x + 54 \quad \text{
✔ Correct}
$$
#### 5. $-6(6x + 7)$
$$
-6 \cdot 6x = -36x,\quad -6 \cdot 7 = -42
\Rightarrow -36x - 42 \quad \text{
✔ Correct}
$$
#### 6. $-2(-9x + 4)$
$$
-2 \cdot (-9x) = 18x,\quad -2 \cdot 4 = -8
\Rightarrow 18x - 8 \quad \text{
✔ Correct}
$$
#### 7. $-7(-6x + 2)$
$$
-7 \cdot (-6x) = 42x,\quad -7 \cdot 2 = -14
\Rightarrow 42x - 14 \quad \text{
✔ Correct}
$$
#### 8. $-8(-8x + 3)$
$$
-8 \cdot (-8x) = 64x,\quad -8 \cdot 3 = -24
\Rightarrow 64x - 24 \quad \text{
✔ Correct}
$$
#### 9. $2(3x - 7)$
$$
2 \cdot 3x = 6x,\quad 2 \cdot (-7) = -14
\Rightarrow 6x - 14 \quad \text{
✔ Correct}
$$
#### 10. $-4(-9x - 2)$
$$
-4 \cdot (-9x) = 36x,\quad -4 \cdot (-2) = 8
\Rightarrow 36x + 8 \quad \text{
✔ Correct}
$$
---
🔹 Part 2: Factor (Factoring Out GCF)
We reverse the distributive property:
> $ ab + ac = a(b + c) $
#### 1. $24x - 48$
Find GCF of 24 and 48 → 24
$$
24x - 48 = 24(x - 2) \quad \text{
✔ Correct}
$$
#### 2. $10x - 25$
GCF of 10 and 25 → 5
$$
10x - 25 = 5(2x - 5) \quad \text{
✔ Correct}
$$
#### 3. $24x + 32$
GCF of 24 and 32 → 8
$$
24x + 32 = 8(3x + 4) \quad \text{
✔ Correct}
$$
#### 4. $-16x + 48$
GCF of 16 and 48 → 16, but both terms are positive in magnitude; sign matters.
We can factor out $-16$ to make the inside simpler:
$$
-16x + 48 = -16(x - 3) \quad \text{
✔ Correct}
$$
(Note: $-16(x - 3) = -16x + 48$, which matches.)
---
✔ Final Summary
All the problems on this worksheet are
correctly solved!
They demonstrate:
-
Distribution: Multiplying a term outside parentheses by each term inside.
-
Factoring: Pulling out the greatest common factor and writing the expression as a product.
These are foundational algebra skills that help simplify expressions and solve equations.
---
📝 Tips for Students:
- Always distribute to
both terms inside the parentheses.
- Pay close attention to
signs, especially when multiplying negative numbers.
- When factoring, find the
largest number that divides all terms, and include the variable with the lowest exponent if applicable.
- Check your work by distributing again to see if you get back the original expression.
Let me know if you'd like practice problems or explanations for more advanced topics!
Parent Tip: Review the logic above to help your child master the concept of simple algebra equations worksheet.
