Distributive Property Worksheets with Answer Key - Free Printable

Let's solve each expression by factoring using the distributive property. The goal is to find the greatest common factor (GCF) of the terms and then factor it out.

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🔹 Distributive Property Review:

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

When factoring, we reverse this:
> $ ab + ac = a(b + c) $

So, we look for the largest number that divides both terms, and then factor it out.

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Let’s go through each problem:

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1. $ 14 + 28d $

- GCF of 14 and 28 is 14
- Factor out 14:
$$
14(1 + 2d)
$$

✔ Answer: $ \boxed{14(1 + 2d)} $

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2. $ 12v + 20 $

- GCF of 12 and 20 is 4
- Factor out 4:
$$
4(3v + 5)
$$

✔ Answer: $ \boxed{4(3v + 5)} $

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3. $ 96m + 80 $

- GCF of 96 and 80 is 16
- Factor out 16:
$$
16(6m + 5)
$$

✔ Answer: $ \boxed{16(6m + 5)} $

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4. $ 120 + 108a $

- GCF of 120 and 108 is 12
- Factor out 12:
$$
12(10 + 9a)
$$

✔ Answer: $ \boxed{12(10 + 9a)} $

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5. $ 24 + 44q $

- GCF of 24 and 44 is 4
- Factor out 4:
$$
4(6 + 11q)
$$

✔ Answer: $ \boxed{4(6 + 11q)} $

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6. $ 132 + 108y $

- GCF of 132 and 108 is 12
- Factor out 12:
$$
12(11 + 9y)
$$

✔ Answer: $ \boxed{12(11 + 9y)} $

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7. $ 12r + 28 $

- GCF of 12 and 28 is 4
- Factor out 4:
$$
4(3r + 7)
$$

✔ Answer: $ \boxed{4(3r + 7)} $

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8. $ 14n + 12 $

- GCF of 14 and 12 is 2
- Factor out 2:
$$
2(7n + 6)
$$

✔ Answer: $ \boxed{2(7n + 6)} $

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9. $ -5f - 35 $

- Both terms are negative; GCF of 5 and 35 is 5
- Factor out -5 (to make inside parentheses positive):
$$
-5(f + 7)
$$

✔ Answer: $ \boxed{-5(f + 7)} $

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10. $ -8h - 32 $

- GCF of 8 and 32 is 8
- Factor out -8:
$$
-8(h + 4)
$$

✔ Answer: $ \boxed{-8(h + 4)} $

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✔ Final Answers Summary:

| Problem | Factored Form |
|--------|----------------|
| 1 | $ 14(1 + 2d) $ |
| 2 | $ 4(3v + 5) $ |
| 3 | $ 16(6m + 5) $ |
| 4 | $ 12(10 + 9a) $ |
| 5 | $ 4(6 + 11q) $ |
| 6 | $ 12(11 + 9y) $ |
| 7 | $ 4(3r + 7) $ |
| 8 | $ 2(7n + 6) $ |
| 9 | $ -5(f + 7) $ |
| 10 | $ -8(h + 4) $ |

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Let me know if you'd like these explained step-by-step with GCF breakdowns!