Math worksheet practicing the distributive property with 30 algebraic expressions to simplify.

Let's solve each expression using the distributive property, which states:

> $ a(b + c) = ab + ac $

This means we multiply the term outside the parentheses by each term inside the parentheses.

We'll go through each problem step-by-step.

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1) $ -(-3 - 6z) $

Distribute the negative sign:
$$
= -(-3) - (-6z) = 3 + 6z
$$
✔ Answer: $ 3 + 6z $

---

2) $ -13(20 - 8z) $

Distribute $-13$:
$$
= -13 \cdot 20 + (-13) \cdot (-8z) = -260 + 104z
$$
✔ Answer: $ -260 + 104z $

---

3) $ -8(11 + 6z) $

Distribute $-8$:
$$
= -8 \cdot 11 + (-8) \cdot 6z = -88 - 48z
$$
✔ Answer: $ -88 - 48z $

---

4) $ -(7 - 4x) $

Distribute the negative sign:
$$
= -7 + 4x
$$
✔ Answer: $ -7 + 4x $

---

5) $ -(20 - 5z) $

Distribute the negative sign:
$$
= -20 + 5z
$$
✔ Answer: $ -20 + 5z $

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6) $ 12(12 + 2x) $

Distribute $12$:
$$
= 12 \cdot 12 + 12 \cdot 2x = 144 + 24x
$$
✔ Answer: $ 144 + 24x $

---

7) $ -3(4 - 6z) $

Distribute $-3$:
$$
= -3 \cdot 4 + (-3) \cdot (-6z) = -12 + 18z
$$
✔ Answer: $ -12 + 18z $

---

8) $ -6(3 - 8x) $

Distribute $-6$:
$$
= -6 \cdot 3 + (-6) \cdot (-8x) = -18 + 48x
$$
✔ Answer: $ -18 + 48x $

---

9) $ 20(20 + 2x) $

Distribute $20$:
$$
= 20 \cdot 20 + 20 \cdot 2x = 400 + 40x
$$
✔ Answer: $ 400 + 40x $

---

10) $ -(3 - 2x) $

Distribute the negative:
$$
= -3 + 2x
$$
✔ Answer: $ -3 + 2x $

---

11) $ -(-21 - 6x) $

Distribute the negative:
$$
= 21 + 6x
$$
✔ Answer: $ 21 + 6x $

---

12) $ -3(9 - 7x) $

Distribute $-3$:
$$
= -3 \cdot 9 + (-3) \cdot (-7x) = -27 + 21x
$$
✔ Answer: $ -27 + 21x $

---

13) $ -(21 - 6x) $

Distribute the negative:
$$
= -21 + 6x
$$
✔ Answer: $ -21 + 6x $

---

14) $ -3(7 + 7x) $

Distribute $-3$:
$$
= -3 \cdot 7 + (-3) \cdot 7x = -21 - 21x
$$
✔ Answer: $ -21 - 21x $

---

15) $ -16(17 + 4x) $

Distribute $-16$:
$$
= -16 \cdot 17 + (-16) \cdot 4x = -272 - 64x
$$
✔ Answer: $ -272 - 64x $

---

16) $ -(6 - 7x) $

Distribute the negative:
$$
= -6 + 7x
$$
✔ Answer: $ -6 + 7x $

---

17) $ 20(21 + 3x) $

Distribute $20$:
$$
= 20 \cdot 21 + 20 \cdot 3x = 420 + 60x
$$
✔ Answer: $ 420 + 60x $

---

18) $ -4(5 - 2x) $

Distribute $-4$:
$$
= -4 \cdot 5 + (-4) \cdot (-2x) = -20 + 8x
$$
✔ Answer: $ -20 + 8x $

---

19) $ -20(21 + 4x) $

Distribute $-20$:
$$
= -20 \cdot 21 + (-20) \cdot 4x = -420 - 80x
$$
✔ Answer: $ -420 - 80x $

---

20) $ -(-17 - 3x) $

Distribute the negative:
$$
= 17 + 3x
$$
✔ Answer: $ 17 + 3x $

---

21) $ -7(2 - 8x) $

Distribute $-7$:
$$
= -7 \cdot 2 + (-7) \cdot (-8x) = -14 + 56x
$$
✔ Answer: $ -14 + 56x $

---

22) $ -14(15 + 4x) $

Distribute $-14$:
$$
= -14 \cdot 15 + (-14) \cdot 4x = -210 - 56x
$$
✔ Answer: $ -210 - 56x $

---

23) $ -10(11 - 2x) $

Distribute $-10$:
$$
= -10 \cdot 11 + (-10) \cdot (-2x) = -110 + 20x
$$
✔ Answer: $ -110 + 20x $

---

24) $ -(-5 - 3x) $

Distribute the negative:
$$
= 5 + 3x
$$
✔ Answer: $ 5 + 3x $

---

25) $ -12(16 - 5x) $

Distribute $-12$:
$$
= -12 \cdot 16 + (-12) \cdot (-5x) = -192 + 60x
$$
✔ Answer: $ -192 + 60x $

---

26) $ 2(5 + 5x) $

Distribute $2$:
$$
= 2 \cdot 5 + 2 \cdot 5x = 10 + 10x
$$
✔ Answer: $ 10 + 10x $

---

27) $ -(-2 - 2x) $

Distribute the negative:
$$
= 2 + 2x
$$
✔ Answer: $ 2 + 2x $

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28) $ 2(2 + 2x) $

Distribute $2$:
$$
= 2 \cdot 2 + 2 \cdot 2x = 4 + 4x
$$
✔ Answer: $ 4 + 4x $

---

29) $ -(-19 - 2x) $

Distribute the negative:
$$
= 19 + 2x
$$
✔ Answer: $ 19 + 2x $

---

30) $ 12(18 + 8x) $

Distribute $12$:
$$
= 12 \cdot 18 + 12 \cdot 8x = 216 + 96x
$$
✔ Answer: $ 216 + 96x $

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✔ Final Answers (Listed):

| Problem | Answer |
|--------|--------|
| 1) | $ 3 + 6z $ |
| 2) | $ -260 + 104z $ |
| 3) | $ -88 - 48z $ |
| 4) | $ -7 + 4x $ |
| 5) | $ -20 + 5z $ |
| 6) | $ 144 + 24x $ |
| 7) | $ -12 + 18z $ |
| 8) | $ -18 + 48x $ |
| 9) | $ 400 + 40x $ |
|10) | $ -3 + 2x $ |
|11) | $ 21 + 6x $ |
|12) | $ -27 + 21x $ |
|13) | $ -21 + 6x $ |
|14) | $ -21 - 21x $ |
|15) | $ -272 - 64x $ |
|16) | $ -6 + 7x $ |
|17) | $ 420 + 60x $ |
|18) | $ -20 + 8x $ |
|19) | $ -420 - 80x $ |
|20) | $ 17 + 3x $ |
|21) | $ -14 + 56x $ |
|22) | $ -210 - 56x $ |
|23) | $ -110 + 20x $ |
|24) | $ 5 + 3x $ |
|25) | $ -192 + 60x $ |
|26) | $ 10 + 10x $ |
|27) | $ 2 + 2x $ |
|28) | $ 4 + 4x $ |
|29) | $ 19 + 2x $ |
|30) | $ 216 + 96x $ |

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🔍 Summary of Key Concepts:

- The distributive property allows us to remove parentheses by multiplying.
- When distributing a negative sign, it changes the sign of every term inside.
- Always remember: $ a(b + c) = ab + ac $
- Pay attention to signs, especially with negatives!

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