Free custom combining like terms worksheet templates - Free Printable

Let's solve each problem step by step. The goal is to distribute and then combine like terms.

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

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

So:
$$
30x - 36 - 12x - 6
$$

Combine like terms:
- $ 30x - 12x = 18x $
- $ -36 - 6 = -42 $

✔ Answer: $ 18x - 42 $

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

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

So:
$$
14x + 77 - 42x + 18
$$

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

✔ Answer: $ -28x + 95 $

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

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

So:
$$
36x + 48 - 15x + 24
$$

Combine like terms:
- $ 36x - 15x = 21x $
- $ 48 + 24 = 72 $

✔ Answer: $ 21x + 72 $

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

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

So:
$$
8x + 32 - 21x + 42
$$

Combine like terms:
- $ 8x - 21x = -13x $
- $ 32 + 42 = 74 $

✔ Answer: $ -13x + 74 $

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

Distribute:
- $ 6 \cdot 2x = 12x $
- $ 6 \cdot 7 = 42 $
- $ 5 \cdot 8x = 40x $
- $ 5 \cdot 1 = 5 $

So:
$$
12x + 42 + 40x + 5
$$

Combine like terms:
- $ 12x + 40x = 52x $
- $ 42 + 5 = 47 $

✔ Answer: $ 52x + 47 $

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

Note: The minus sign before the parentheses means we distribute $-1$.

Distribute:
- $ 5 \cdot x = 5x $
- $ 5 \cdot (-10) = -50 $
- $ -1 \cdot 2x = -2x $
- $ -1 \cdot 6 = -6 $

So:
$$
5x - 50 - 2x - 6
$$

Combine like terms:
- $ 5x - 2x = 3x $
- $ -50 - 6 = -56 $

✔ Answer: $ 3x - 56 $

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

Distribute:
- $ 3 \cdot x = 3x $
- $ 3 \cdot (-2) = -6 $
- $ -4 \cdot 5x = -20x $
- $ -4 \cdot (-8) = +32 $

So:
$$
3x - 6 - 20x + 32
$$

Combine like terms:
- $ 3x - 20x = -17x $
- $ -6 + 32 = 26 $

✔ Answer: $ -17x + 26 $

---

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

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

So:
$$
42x - 14 - 8x - 64
$$

Combine like terms:
- $ 42x - 8x = 34x $
- $ -14 - 64 = -78 $

✔ Answer: $ 34x - 78 $

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

Distribute:
- $ 5 \cdot 3x = 15x $
- $ 5 \cdot 10 = 50 $
- $ 3 \cdot x = 3x $
- $ 3 \cdot 8 = 24 $

So:
$$
15x + 50 + 3x + 24
$$

Combine like terms:
- $ 15x + 3x = 18x $
- $ 50 + 24 = 74 $

✔ Answer: $ 18x + 74 $

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

Distribute:
- $ 7 \cdot x = 7x $
- $ 7 \cdot 2 = 14 $
- $ 6 \cdot 3x = 18x $
- $ 6 \cdot (-7) = -42 $

So:
$$
7x + 14 + 18x - 42
$$

Combine like terms:
- $ 7x + 18x = 25x $
- $ 14 - 42 = -28 $

✔ Answer: $ 25x - 28 $

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✔ Final Answers:

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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