Factor Using the Distributive Property | Worksheet - Free Printable

Let's solve the problem step by step using the distributive property and greatest common factor (GCF).

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🔍 What is the Distributive Property?

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

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

We use the GCF of the terms to factor out the common part.

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✔ Example Given in the Worksheet

Expression: $ 40 + 16 $

- GCF of 40 and 16 is 8
- Rewrite each term as a product with the GCF:
- $ 40 = 8 \times 5 $
- $ 16 = 8 \times 2 $
- So: $ 40 + 16 = 8(5 + 2) $

✔ Check: $ 8 \times 5 = 40 $, $ 8 \times 2 = 16 $ → Correct!

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Now let’s go through each problem on the worksheet.

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📌 Problem Set

#### 1. $ 8 + 12 $
- GCF of 8 and 12 is 4
- $ 8 = 4 \times 2 $, $ 12 = 4 \times 3 $
- So: $ 8 + 12 = 4(2 + 3) $
- ✔ Check: $ 4 \times 2 = 8 $, $ 4 \times 3 = 12 $ → ✔️

> Answer: $ 4(2 + 3) $

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#### 2. $ 21 + 15 $
- GCF of 21 and 15 is 3
- $ 21 = 3 \times 7 $, $ 15 = 3 \times 5 $
- So: $ 21 + 15 = 3(7 + 5) $
- ✔ Check: $ 3 \times 7 = 21 $, $ 3 \times 5 = 15 $ → ✔️

> Answer: $ 3(7 + 5) $

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#### 3. $ 24 + 30 $
- GCF of 24 and 30 is 6
- $ 24 = 6 \times 4 $, $ 30 = 6 \times 5 $
- So: $ 24 + 30 = 6(4 + 5) $
- ✔ Check: $ 6 \times 4 = 24 $, $ 6 \times 5 = 30 $ → ✔️

> Answer: $ 6(4 + 5) $

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#### 4. $ 30 + 18 $
- GCF of 30 and 18 is 6
- $ 30 = 6 \times 5 $, $ 18 = 6 \times 3 $
- So: $ 30 + 18 = 6(5 + 3) $
- ✔ Check: $ 6 \times 5 = 30 $, $ 6 \times 3 = 18 $ → ✔️

> Answer: $ 6(5 + 3) $

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#### 5. $ 27 + 36 $
- GCF of 27 and 36 is 9
- $ 27 = 9 \times 3 $, $ 36 = 9 \times 4 $
- So: $ 27 + 36 = 9(3 + 4) $
- ✔ Check: $ 9 \times 3 = 27 $, $ 9 \times 4 = 36 $ → ✔️

> Answer: $ 9(3 + 4) $

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#### 6. $ 35 + 50 $
- GCF of 35 and 50 is 5
- $ 35 = 5 \times 7 $, $ 50 = 5 \times 10 $
- So: $ 35 + 50 = 5(7 + 10) $
- ✔ Check: $ 5 \times 7 = 35 $, $ 5 \times 10 = 50 $ → ✔️

> Answer: $ 5(7 + 10) $

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#### 7. $ 32 + 48 $
- GCF of 32 and 48 is 16
- $ 32 = 16 \times 2 $, $ 48 = 16 \times 3 $
- So: $ 32 + 48 = 16(2 + 3) $
- ✔ Check: $ 16 \times 2 = 32 $, $ 16 \times 3 = 48 $ → ✔️

> Answer: $ 16(2 + 3) $

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#### 8. $ 40 + 72 $
- GCF of 40 and 72 is 8
- $ 40 = 8 \times 5 $, $ 72 = 8 \times 9 $
- So: $ 40 + 72 = 8(5 + 9) $
- ✔ Check: $ 8 \times 5 = 40 $, $ 8 \times 9 = 72 $ → ✔️

> Answer: $ 8(5 + 9) $

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#### 9. $ 56 + 42 $
- GCF of 56 and 42 is 14
- $ 56 = 14 \times 4 $, $ 42 = 14 \times 3 $
- So: $ 56 + 42 = 14(4 + 3) $
- ✔ Check: $ 14 \times 4 = 56 $, $ 14 \times 3 = 42 $ → ✔️

> Answer: $ 14(4 + 3) $

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✔ Final Answers Table:

| Expression | GCF | Factored Form |
|----------|-----|----------------|
| 8 + 12 | 4 | 4(2 + 3) |
| 21 + 15 | 3 | 3(7 + 5) |
| 24 + 30 | 6 | 6(4 + 5) |
| 30 + 18 | 6 | 6(5 + 3) |
| 27 + 36 | 9 | 9(3 + 4) |
| 35 + 50 | 5 | 5(7 + 10) |
| 32 + 48 | 16 | 16(2 + 3) |
| 40 + 72 | 8 | 8(5 + 9) |
| 56 + 42 | 14 | 14(4 + 3) |

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💡 Tips for Success:

- Always find the GCF first.
- Divide each number by the GCF to get the numbers inside the parentheses.
- Use the distributive property in reverse: $ ab + ac = a(b + c) $
- Double-check by distributing back.

Let me know if you'd like this turned into a printable answer key!