Worksheet for practicing the distributive property and factoring with algebraic expressions.

Absolutely! Let’s solve both columns of this worksheet step by step.

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## 🔹 Left Column: Use the Distributive Property to Rewrite the Expression

The distributive property says:
> a(b + c) = ab + ac
> or
> a(b - c) = ab - ac

We multiply the number outside the parentheses by each term inside.

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1. 5(x + 3)

= 5·x + 5·3
= 5x + 15

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2. 4(2 + m)

= 4·2 + 4·m
= 8 + 4m

*(You can also write it as 4m + 8 — order doesn’t matter in addition)*

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3. 6(v + 4)

= 6·v + 6·4
= 6v + 24

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4. 2(b - 5)

= 2·b - 2·5
= 2b - 10

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5. 7(3 - n)

= 7·3 - 7·n
= 21 - 7n

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6. 3(8n - 3m)

= 3·8n - 3·3m
= 24n - 9m

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7. 8(3t - 2g)

= 8·3t - 8·2g
= 24t - 16g

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8. (2 + 3q)4

*(Note: The 4 is on the outside — same as 4(2 + 3q))*

= 4·2 + 4·3q
= 8 + 12q

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9. (8 - 5n)3

= 3·8 - 3·5n
= 24 - 15n

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10. (12r + 7m)2

= 2·12r + 2·7m
= 24r + 14m

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✔ Left Column Answers Summary:

1. 5x + 15
2. 8 + 4m
3. 6v + 24
4. 2b - 10
5. 21 - 7n
6. 24n - 9m
7. 24t - 16g
8. 8 + 12q
9. 24 - 15n
10. 24r + 14m

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## 🔹 Right Column: Use the GCF to Rewrite the Expression

GCF = Greatest Common Factor — the largest number (and variable, if applicable) that divides evenly into all terms.

We factor out the GCF and write the expression as:
> GCF × (remaining terms)

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1. 48 + 6m

- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 6: 1, 2, 3, 6
→ GCF of numbers = 6

No common variable → GCF = 6

Factor out 6:

= 6(8) + 6(m)
= 6(8 + m)

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2. 20r + 16z

- GCF of 20 and 16:
20 = 2×2×5
16 = 2×2×2×2
→ GCF = 4

No common variable → GCF = 4

= 4(5r) + 4(4z)
= 4(5r + 4z)

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3. 14n + 12p

- GCF of 14 and 12:
14 = 2×7
12 = 2×2×3
→ GCF = 2

No common variable → GCF = 2

= 2(7n) + 2(6p)
= 2(7n + 6p)

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4. 36 - 9z

- GCF of 36 and 9:
36 = 2×2×3×3
9 = 3×3
→ GCF = 9

= 9(4) - 9(z)
= 9(4 - z)

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5. 24x - 18y

- GCF of 24 and 18:
24 = 2×2×2×3
18 = 2×3×3
→ GCF = 6

= 6(4x) - 6(3y)
= 6(4x - 3y)

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6. 8x - 6t

- GCF of 8 and 6:
8 = 2×2×2
6 = 2×3
→ GCF = 2

= 2(4x) - 2(3t)
= 2(4x - 3t)

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7. 21 + 14y

- GCF of 21 and 14:
21 = 3×7
14 = 2×7
→ GCF = 7

= 7(3) + 7(2y)
= 7(3 + 2y)

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8. 26p - 13h

- GCF of 26 and 13:
26 = 2×13
13 = 13
→ GCF = 13

= 13(2p) - 13(h)
= 13(2p - h)

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9. 6 - 9z

- GCF of 6 and 9:
6 = 2×3
9 = 3×3
→ GCF = 3

= 3(2) - 3(3z)
= 3(2 - 3z)

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10. 96g + 80f

- GCF of 96 and 80:

Break down:
- 96 = 2×2×2×2×2×3
- 80 = 2×2×2×2×5
→ GCF = 16

= 16(6g) + 16(5f)
= 16(6g + 5f)

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✔ Right Column Answers Summary:

1. 6(8 + m)
2. 4(5r + 4z)
3. 2(7n + 6p)
4. 9(4 - z)
5. 6(4x - 3y)
6. 2(4x - 3t)
7. 7(3 + 2y)
8. 13(2p - h)
9. 3(2 - 3z)
10. 16(6g + 5f)

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## 🎯 Final Answer Key:

Left Column (Distributive Property):

1. 5x + 15
2. 8 + 4m
3. 6v + 24
4. 2b - 10
5. 21 - 7n
6. 24n - 9m
7. 24t - 16g
8. 8 + 12q
9. 24 - 15n
10. 24r + 14m

Right Column (Factoring using GCF):

1. 6(8 + m)
2. 4(5r + 4z)
3. 2(7n + 6p)
4. 9(4 - z)
5. 6(4x - 3y)
6. 2(4x - 3t)
7. 7(3 + 2y)
8. 13(2p - h)
9. 3(2 - 3z)
10. 16(6g + 5f)

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Let me know if you’d like a printable version or explanations with diagrams! 😊