Algebra worksheet for combining like terms, focusing on distributing and simplifying expressions.

Let's solve each problem step by step. The goal is to distribute (use the distributive property) and then combine like terms.

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1. $ 6(5x - 6) - 6(2x + 1) $

Step 1: Distribute
$$
6 \cdot 5x = 30x,\quad 6 \cdot (-6) = -36
$$
$$
-6 \cdot 2x = -12x,\quad -6 \cdot 1 = -6
$$
So:
$$
30x - 36 - 12x - 6
$$

Step 2: Combine like terms
$$
(30x - 12x) + (-36 - 6) = 18x - 42
$$

✔ Answer: $ 18x - 42 $

---

2. $ 7(2x + 11) - 6(7x - 3) $

Distribute:
$$
7 \cdot 2x = 14x,\quad 7 \cdot 11 = 77
$$
$$
-6 \cdot 7x = -42x,\quad -6 \cdot (-3) = +18
$$
So:
$$
14x + 77 - 42x + 18
$$

Combine like terms:
$$
(14x - 42x) + (77 + 18) = -28x + 95
$$

✔ Answer: $ -28x + 95 $

---

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

Distribute:
$$
6 \cdot 6x = 36x,\quad 6 \cdot 8 = 48
$$
$$
-3 \cdot 5x = -15x,\quad -3 \cdot (-8) = +24
$$
So:
$$
36x + 48 - 15x + 24
$$

Combine:
$$
(36x - 15x) + (48 + 24) = 21x + 72
$$

✔ Answer: $ 21x + 72 $

---

4. $ 4(2x + 8) - 7(3x - 6) $

Distribute:
$$
4 \cdot 2x = 8x,\quad 4 \cdot 8 = 32
$$
$$
-7 \cdot 3x = -21x,\quad -7 \cdot (-6) = +42
$$
So:
$$
8x + 32 - 21x + 42
$$

Combine:
$$
(8x - 21x) + (32 + 42) = -13x + 74
$$

✔ Answer: $ -13x + 74 $

---

5. $ 6(2x + 7) + 5(8x + 1) $

Distribute:
$$
6 \cdot 2x = 12x,\quad 6 \cdot 7 = 42
$$
$$
5 \cdot 8x = 40x,\quad 5 \cdot 1 = 5
$$
So:
$$
12x + 42 + 40x + 5
$$

Combine:
$$
(12x + 40x) + (42 + 5) = 52x + 47
$$

✔ Answer: $ 52x + 47 $

---

6. $ 5(x - 10) - (2x + 6) $

Note: The minus sign before the parentheses means subtract each term inside.

Distribute:
$$
5 \cdot x = 5x,\quad 5 \cdot (-10) = -50
$$
$$
-(2x + 6) = -2x - 6
$$
So:
$$
5x - 50 - 2x - 6
$$

Combine:
$$
(5x - 2x) + (-50 - 6) = 3x - 56
$$

✔ Answer: $ 3x - 56 $

---

7. $ 3(x - 2) - 4(5x - 8) $

Distribute:
$$
3x - 6
$$
$$
-4 \cdot 5x = -20x,\quad -4 \cdot (-8) = +32
$$
So:
$$
3x - 6 - 20x + 32
$$

Combine:
$$
(3x - 20x) + (-6 + 32) = -17x + 26
$$

✔ Answer: $ -17x + 26 $

---

8. $ 7(6x - 2) - 8(x + 8) $

Distribute:
$$
7 \cdot 6x = 42x,\quad 7 \cdot (-2) = -14
$$
$$
-8 \cdot x = -8x,\quad -8 \cdot 8 = -64
$$
So:
$$
42x - 14 - 8x - 64
$$

Combine:
$$
(42x - 8x) + (-14 - 64) = 34x - 78
$$

✔ Answer: $ 34x - 78 $

---

9. $ 5(3x + 10) + 3(x + 8) $

Distribute:
$$
5 \cdot 3x = 15x,\quad 5 \cdot 10 = 50
$$
$$
3 \cdot x = 3x,\quad 3 \cdot 8 = 24
$$
So:
$$
15x + 50 + 3x + 24
$$

Combine:
$$
(15x + 3x) + (50 + 24) = 18x + 74
$$

✔ Answer: $ 18x + 74 $

---

10. $ 7(x + 2) + 6(3x - 7) $

Distribute:
$$
7x + 14
$$
$$
6 \cdot 3x = 18x,\quad 6 \cdot (-7) = -42
$$
So:
$$
7x + 14 + 18x - 42
$$

Combine:
$$
(7x + 18x) + (14 - 42) = 25x - 28
$$

✔ Answer: $ 25x - 28 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 18x - 42 $ |
| 2 | $ -28x + 95 $ |
| 3 | $ 21x + 72 $ |
| 4 | $ -13x + 74 $ |
| 5 | $ 52x + 47 $ |
| 6 | $ 3x - 56 $ |
| 7 | $ -17x + 26 $ |
| 8 | $ 34x - 78 $ |
| 9 | $ 18x + 74 $ |
| 10 | $ 25x - 28 $ |

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🔍 Key Steps Recap:

1. Distribute the number outside the parentheses to each term inside.
2. Simplify signs carefully, especially with subtraction.
3. Combine like terms: add or subtract coefficients of the same variable and constants separately.

Let me know if you'd like a printable version or explanations in a different format!