Distributive Property II. Interactive worksheet | TopWorksheets - Free Printable

Let's solve each problem step by step using the distributive property and then combine like terms. The distributive property states:

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

We’ll apply this to each expression, simplify, and combine like terms.

---

1. $ 2(5x + 10) $

Distribute the 2:
$$
2 \cdot 5x = 10x,\quad 2 \cdot 10 = 20
$$
So:
$$
10x + 20
$$

✔ Answer: $ 10x + 20 $

---

2. $ -6(6 + 4x) $

Distribute the -6:
$$
-6 \cdot 6 = -36,\quad -6 \cdot 4x = -24x
$$
So:
$$
-36 - 24x
$$

We can write it as: $ -24x - 36 $

✔ Answer: $ -24x - 36 $

---

3. $ 9(-7y + 5) $

Distribute the 9:
$$
9 \cdot (-7y) = -63y,\quad 9 \cdot 5 = 45
$$
So:
$$
-63y + 45
$$

✔ Answer: $ -63y + 45 $

---

4. $ -x - (1 + 8x) $

First, distribute the negative sign (which is like multiplying by -1):
$$
-x - 1 - 8x
$$

Now combine like terms:
$$
(-x - 8x) - 1 = -9x - 1
$$

✔ Answer: $ -9x - 1 $

---

5. $ 6(n - 8) - 9(1 - 10n) $

Distribute both:
- $ 6(n - 8) = 6n - 48 $
- $ -9(1 - 10n) = -9 + 90n $

Now combine:
$$
6n - 48 - 9 + 90n = (6n + 90n) + (-48 - 9) = 96n - 57
$$

✔ Answer: $ 96n - 57 $

---

6. $ 4g + 3(g - 1) $

Distribute the 3:
$$
3(g - 1) = 3g - 3
$$

Now add:
$$
4g + 3g - 3 = 7g - 3
$$

✔ Answer: $ 7g - 3 $

---

7. $ -(x + 3) + 8(1 - 6x) $

Distribute:
- $ -(x + 3) = -x - 3 $
- $ 8(1 - 6x) = 8 - 48x $

Now combine:
$$
-x - 3 + 8 - 48x = (-x - 48x) + (-3 + 8) = -49x + 5
$$

✔ Answer: $ -49x + 5 $

---

8. $ -9(1 - 9a) + 7(2 + 9a) $

Distribute:
- $ -9(1 - 9a) = -9 + 81a $
- $ 7(2 + 9a) = 14 + 63a $

Combine:
$$
(-9 + 14) + (81a + 63a) = 5 + 144a
$$

Or: $ 144a + 5 $

✔ Answer: $ 144a + 5 $

---

9. $ -7(8 + 8x) - 6x $

Distribute:
- $ -7(8 + 8x) = -56 - 56x $

Now subtract $ 6x $:
$$
-56 - 56x - 6x = -56 - 62x
$$

Or: $ -62x - 56 $

✔ Answer: $ -62x - 56 $

---

10. $ 10(n + 5) - 5n $

Distribute:
- $ 10(n + 5) = 10n + 50 $

Now subtract $ 5n $:
$$
10n + 50 - 5n = (10n - 5n) + 50 = 5n + 50
$$

✔ Answer: $ 5n + 50 $

---

11. $ -4(1 - 8x) - 4(8x + 4) $

Distribute both:
- $ -4(1 - 8x) = -4 + 32x $
- $ -4(8x + 4) = -32x - 16 $

Now combine:
$$
(-4 + 32x) + (-32x - 16) = 32x - 32x + (-4 - 16) = 0x - 20 = -20
$$

✔ Answer: $ -20 $

---

12. $ -(3p + 2) - 3(5p + 7) $

Distribute:
- $ -(3p + 2) = -3p - 2 $
- $ -3(5p + 7) = -15p - 21 $

Now combine:
$$
-3p - 2 - 15p - 21 = (-3p - 15p) + (-2 - 21) = -18p - 23
$$

✔ Answer: $ -18p - 23 $

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 10x + 20 $ |
| 2 | $ -24x - 36 $ |
| 3 | $ -63y + 45 $ |
| 4 | $ -9x - 1 $ |
| 5 | $ 96n - 57 $ |
| 6 | $ 7g - 3 $ |
| 7 | $ -49x + 5 $ |
| 8 | $ 144a + 5 $ |
| 9 | $ -62x - 56 $ |
| 10 | $ 5n + 50 $ |
| 11 | $ -20 $ |
| 12 | $ -18p - 23 $ |

Let me know if you'd like these explained in a video or with visual steps!