Distributive Property And Factoring Worksheet Worksheet - Free Printable

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

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## Left Column: Use the Distributive Property to rewrite the expression

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

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

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1. 5(x + 3)

→ 5·x + 5·3 = 5x + 15

2. 4(2 + m)

→ 4·2 + 4·m = 8 + 4m

3. 6(v + 4)

→ 6·v + 6·4 = 6v + 24

4. 2(b - 5)

→ 2·b - 2·5 = 2b - 10

5. 7(3 - n)

→ 7·3 - 7·n = 21 - 7n

6. 3(8n - 3m)

→ 3·8n - 3·3m = 24n - 9m

7. 8(3t - 2g)

→ 8·3t - 8·2g = 24t - 16g

8. (2 + 3q)4

*(Note: The 4 is outside, so we distribute 4 to both terms)*
→ 4·2 + 4·3q = 8 + 12q

*(Alternatively, you could write it as 4(2 + 3q) — same result.)*

9. (8 - 5n)3

→ 3·8 - 3·5n = 24 - 15n

10. (12r + 7m)2

→ 2·12r + 2·7m = 24r + 14m

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✔ Left Column Answers:

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 all terms evenly.

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

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1. 48 + 6m

- GCF of 48 and 6 is 6
- 48 ÷ 6 = 8
- 6m ÷ 6 = m
→ 6(8 + m)

2. 20r + 16z

- GCF of 20 and 16 is 4
- 20r ÷ 4 = 5r
- 16z ÷ 4 = 4z
→ 4(5r + 4z)

3. 14n + 12p

- GCF of 14 and 12 is 2
- 14n ÷ 2 = 7n
- 12p ÷ 2 = 6p
→ 2(7n + 6p)

4. 36 - 9z

- GCF of 36 and 9 is 9
- 36 ÷ 9 = 4
- 9z ÷ 9 = z
→ 9(4 - z)

*(Note: We keep the minus sign inside the parentheses.)*

5. 24x - 18y

- GCF of 24 and 18 is 6
- 24x ÷ 6 = 4x
- 18y ÷ 6 = 3y
→ 6(4x - 3y)

6. 8x - 6t

- GCF of 8 and 6 is 2
- 8x ÷ 2 = 4x
- 6t ÷ 2 = 3t
→ 2(4x - 3t)

7. 21 + 14y

- GCF of 21 and 14 is 7
- 21 ÷ 7 = 3
- 14y ÷ 7 = 2y
→ 7(3 + 2y)

8. 26p - 13h

- GCF of 26 and 13 is 13
- 26p ÷ 13 = 2p
- 13h ÷ 13 = h
→ 13(2p - h)

9. 6 - 9z

- GCF of 6 and 9 is 3
- 6 ÷ 3 = 2
- 9z ÷ 3 = 3z
→ 3(2 - 3z)

10. 96g + 80f

- GCF of 96 and 80 is 16
- 96g ÷ 16 = 6g
- 80f ÷ 16 = 5f
→ 16(6g + 5f)

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✔ Right Column Answers:

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 Summary:

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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