The Distributive Property worksheets - Free Printable

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

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

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

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

---

1) $ 13(15 + 4x) $

$$
= 13 \cdot 15 + 13 \cdot 4x = 195 + 52x
$$

✔ Answer: $ 195 + 52x $

---

2) $ -13(13 + 3x) $

$$
= -13 \cdot 13 + (-13) \cdot 3x = -169 - 39x
$$

✔ Answer: $ -169 - 39x $

---

3) $ -5(6 + 8x) $

$$
= -5 \cdot 6 + (-5) \cdot 8x = -30 - 40x
$$

✔ Answer: $ -30 - 40x $

---

4) $ -15(17 - 3x) $

Note: $ -3x $ is the same as $ +(-3x) $
$$
= -15 \cdot 17 + (-15) \cdot (-3x) = -255 + 45x
$$

✔ Answer: $ -255 + 45x $

---

5) $ -(-19 - 2x) $

This is like multiplying by $-1$:
$$
= -1 \cdot (-19) + (-1) \cdot (-2x) = 19 + 2x
$$

✔ Answer: $ 19 + 2x $

---

6) $ -(7 - 4x) $

$$
= -1 \cdot 7 + (-1) \cdot (-4x) = -7 + 4x
$$

✔ Answer: $ -7 + 4x $

---

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

$$
= -3 \cdot 9 + (-3) \cdot (-7x) = -27 + 21x
$$

✔ Answer: $ -27 + 21x $

---

8) $ 20(20 + 2x) $

$$
= 20 \cdot 20 + 20 \cdot 2x = 400 + 40x
$$

✔ Answer: $ 400 + 40x $

---

9) $ -15(20 + 8x) $

$$
= -15 \cdot 20 + (-15) \cdot 8x = -300 - 120x
$$

✔ Answer: $ -300 - 120x $

---

10) $ -6(3 - 8x) $

$$
= -6 \cdot 3 + (-6) \cdot (-8x) = -18 + 48x
$$

✔ Answer: $ -18 + 48x $

---

11) $ -17(19 - 3x) $

$$
= -17 \cdot 19 + (-17) \cdot (-3x) = -323 + 51x
$$

✔ Answer: $ -323 + 51x $

---

12) $ -(-3 - 6x) $

$$
= -1 \cdot (-3) + (-1) \cdot (-6x) = 3 + 6x
$$

✔ Answer: $ 3 + 6x $

---

13) $ -5(5 + 7x) $

$$
= -5 \cdot 5 + (-5) \cdot 7x = -25 - 35x
$$

✔ Answer: $ -25 - 35x $

---

14) $ 12(18 + 8x) $

$$
= 12 \cdot 18 + 12 \cdot 8x = 216 + 96x
$$

✔ Answer: $ 216 + 96x $

---

15) $ -(-5 - 3x) $

$$
= -1 \cdot (-5) + (-1) \cdot (-3x) = 5 + 3x
$$

✔ Answer: $ 5 + 3x $

---

16) $ -(-18 - 7x) $

$$
= -1 \cdot (-18) + (-1) \cdot (-7x) = 18 + 7x
$$

✔ Answer: $ 18 + 7x $

---

17) $ -10(10 + 3x) $

$$
= -10 \cdot 10 + (-10) \cdot 3x = -100 - 30x
$$

✔ Answer: $ -100 - 30x $

---

18) $ -(13 - 3x) $

$$
= -1 \cdot 13 + (-1) \cdot (-3x) = -13 + 3x
$$

✔ Answer: $ -13 + 3x $

---

19) $ 2(7 + 7x) $

$$
= 2 \cdot 7 + 2 \cdot 7x = 14 + 14x
$$

✔ Answer: $ 14 + 14x $

---

20) $ -5(12 - 8x) $

$$
= -5 \cdot 12 + (-5) \cdot (-8x) = -60 + 40x
$$

✔ Answer: $ -60 + 40x $

---

21) $ -(-12 - 6x) $

$$
= -1 \cdot (-12) + (-1) \cdot (-6x) = 12 + 6x
$$

✔ Answer: $ 12 + 6x $

---

22) $ -(-20 - 3x) $

$$
= -1 \cdot (-20) + (-1) \cdot (-3x) = 20 + 3x
$$

✔ Answer: $ 20 + 3x $

---

✔ Final Answers (Summarized):

| Problem | Answer |
|--------|--------|
| 1) | $ 195 + 52x $ |
| 2) | $ -169 - 39x $ |
| 3) | $ -30 - 40x $ |
| 4) | $ -255 + 45x $ |
| 5) | $ 19 + 2x $ |
| 6) | $ -7 + 4x $ |
| 7) | $ -27 + 21x $ |
| 8) | $ 400 + 40x $ |
| 9) | $ -300 - 120x $ |
| 10) | $ -18 + 48x $ |
| 11) | $ -323 + 51x $ |
| 12) | $ 3 + 6x $ |
| 13) | $ -25 - 35x $ |
| 14) | $ 216 + 96x $ |
| 15) | $ 5 + 3x $ |
| 16) | $ 18 + 7x $ |
| 17) | $ -100 - 30x $ |
| 18) | $ -13 + 3x $ |
| 19) | $ 14 + 14x $ |
| 20) | $ -60 + 40x $ |
| 21) | $ 12 + 6x $ |
| 22) | $ 20 + 3x $ |

---

Let me know if you'd like these formatted for printing or need explanations for any specific one!