Worksheet for practicing the distributive property in algebra.

Sure! Let’s solve each expression using the Distributive Property, which states:

> a(b + c) = ab + ac
> or more generally, a(b ± c) = ab ± ac

We’ll go through each problem one by one.

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1. `4(x + 3)`

Multiply 4 by both terms inside the parentheses:
→ `4·x + 4·3 = 4x + 12`

✔ Answer: 4x + 12

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2. `5(x - 2)`

Multiply 5 by both terms:
→ `5·x - 5·2 = 5x - 10`

✔ Answer: 5x - 10

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3. `6(x + 7)`

Multiply 6 by both terms:
→ `6·x + 6·7 = 6x + 42`

✔ Answer: 6x + 42

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4. `-6(x - 10)`

Multiply -6 by both terms:
→ `-6·x + (-6)·(-10) = -6x + 60`
*(Note: negative times negative is positive)*

✔ Answer: -6x + 60

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5. `-3(5 + x)`

Multiply -3 by both terms:
→ `-3·5 + (-3)·x = -15 - 3x`
*(You can also write it as -3x - 15 — same thing)*

✔ Answer: -15 - 3x (or -3x - 15)

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6. `-9(4 - x)`

Multiply -9 by both terms:
→ `-9·4 + (-9)·(-x) = -36 + 9x`
*(Negative times negative gives positive)*

✔ Answer: 9x - 36 *(reordered for standard form)*

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7. `2(4x - 1)`

Multiply 2 by both terms:
→ `2·4x - 2·1 = 8x - 2`

✔ Answer: 8x - 2

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8. `7(5x + 2y)`

Multiply 7 by both terms:
→ `7·5x + 7·2y = 35x + 14y`

✔ Answer: 35x + 14y

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9. `-4(2x - 9)`

Multiply -4 by both terms:
→ `-4·2x + (-4)·(-9) = -8x + 36`

✔ Answer: -8x + 36

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10. `(5x - 8)2`

This is the same as `2(5x - 8)` — just written differently.
Multiply 2 by both terms:
→ `2·5x - 2·8 = 10x - 16`

✔ Answer: 10x - 16

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11. `(-6x + 3)(-7)`

Multiply -7 by both terms:
→ `(-7)·(-6x) + (-7)·3 = 42x - 21`

✔ Answer: 42x - 21

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12. `(-x - 1)4`

Multiply 4 by both terms:
→ `4·(-x) + 4·(-1) = -4x - 4`

✔ Answer: -4x - 4

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## ✔ Final Answers (All Simplified):

1. `4x + 12`
2. `5x - 10`
3. `6x + 42`
4. `-6x + 60`
5. `-15 - 3x` or `-3x - 15`
6. `9x - 36`
7. `8x - 2`
8. `35x + 14y`
9. `-8x + 36`
10. `10x - 16`
11. `42x - 21`
12. `-4x - 4`

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## 💡 Tip:
Always remember to distribute the number (including its sign!) to every term inside the parentheses. Watch out for negative signs — they can change the sign of the result!

Let me know if you’d like to see any step broken down further!