Math worksheet for practicing the distributive property and combining like terms.

Let's solve each expression 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 problem, simplify, and combine like terms.

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1. $ 2(5x + 10) $

Apply distributive property:
$$
2 \cdot 5x + 2 \cdot 10 = 10x + 20
$$

✔ Answer: $ 10x + 20 $

---

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

Distribute $-6$:
$$
-6 \cdot 6 + (-6) \cdot 4x = -36 - 24x
$$

Rewrite in standard form (variable first):
$$
-24x - 36
$$

✔ Answer: $ -24x - 36 $

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

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

✔ Answer: $ -63y + 45 $

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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 $

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

Distribute both terms:
$$
6n - 48 - 9 + 90n
$$

Combine like terms:
$$
(6n + 90n) + (-48 - 9) = 96n - 57
$$

✔ Answer: $ 96n - 57 $

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

Distribute $3$:
$$
4g + 3g - 3 = 7g - 3
$$

✔ Answer: $ 7g - 3 $

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

Distribute the negative and the 8:
$$
- x - 3 + 8 - 48x
$$

Combine like terms:
$$
(-x - 48x) + (-3 + 8) = -49x + 5
$$

✔ Answer: $ -49x + 5 $

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

Distribute both:
$$
-9 + 81a + 14 + 63a
$$

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

✔ Answer: $ 144a + 5 $

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

Distribute $-7$:
$$
-56 - 56x - 6x
$$

Combine like terms:
$$
-56 - 62x
$$

Or: $ -62x - 56 $

✔ Answer: $ -62x - 56 $

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

Distribute $10$:
$$
10n + 50 - 5n
$$

Combine like terms:
$$
(10n - 5n) + 50 = 5n + 50
$$

✔ Answer: $ 5n + 50 $

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

Distribute both:
$$
-4 + 32x - 32x - 16
$$

Combine like terms:
$$
(32x - 32x) + (-4 - 16) = 0x - 20 = -20
$$

✔ Answer: $ -20 $

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

Distribute the negative and the $-3$:
$$
-3p - 2 - 15p - 21
$$

Combine like terms:
$$
(-3p - 15p) + (-2 - 21) = -18p - 23
$$

✔ Answer: $ -18p - 23 $

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✔ Final Answers:

| Problem | Simplified Expression |
|--------|------------------------|
| 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 more detail!