Algebra worksheet for practicing distribution and combining like terms.

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

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1.) $ 8(9x - 10) - 8(2x + 1) $

Step 1: Distribute
- $ 8 \cdot 9x = 72x $
- $ 8 \cdot (-10) = -80 $
- $ -8 \cdot 2x = -16x $
- $ -8 \cdot 1 = -8 $

So:
$$
72x - 80 - 16x - 8
$$

Step 2: Combine like terms
- $ 72x - 16x = 56x $
- $ -80 - 8 = -88 $

✔ Answer: $ 56x - 88 $

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

Distribute:
- $ 6 \cdot 2x = 12x $
- $ 6 \cdot 11 = 66 $
- $ -6 \cdot 7x = -42x $
- $ -6 \cdot (-3) = +18 $

So:
$$
12x + 66 - 42x + 18
$$

Combine:
- $ 12x - 42x = -30x $
- $ 66 + 18 = 84 $

✔ Answer: $ -30x + 84 $

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3.) $ 6(4x + 9) - 8(5x - 8) $

Distribute:
- $ 6 \cdot 4x = 24x $
- $ 6 \cdot 9 = 54 $
- $ -8 \cdot 5x = -40x $
- $ -8 \cdot (-8) = +64 $

So:
$$
24x + 54 - 40x + 64
$$

Combine:
- $ 24x - 40x = -16x $
- $ 54 + 64 = 118 $

✔ Answer: $ -16x + 118 $

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4.) $ 8(2x + 7) + 5(10x + 1) $

Distribute:
- $ 8 \cdot 2x = 16x $
- $ 8 \cdot 7 = 56 $
- $ 5 \cdot 10x = 50x $
- $ 5 \cdot 1 = 5 $

So:
$$
16x + 56 + 50x + 5
$$

Combine:
- $ 16x + 50x = 66x $
- $ 56 + 5 = 61 $

✔ Answer: $ 66x + 61 $

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5.) $ 5(2x + 9) - 8(3x - 5) $

Distribute:
- $ 5 \cdot 2x = 10x $
- $ 5 \cdot 9 = 45 $
- $ -8 \cdot 3x = -24x $
- $ -8 \cdot (-5) = +40 $

So:
$$
10x + 45 - 24x + 40
$$

Combine:
- $ 10x - 24x = -14x $
- $ 45 + 40 = 85 $

✔ Answer: $ -14x + 85 $

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6.) $ 6(x - 11) - (3x + 5) $

Note: There's no coefficient in front of the second parentheses, so it's just $ -1(3x + 5) $

Distribute:
- $ 6 \cdot x = 6x $
- $ 6 \cdot (-11) = -66 $
- $ -1 \cdot 3x = -3x $
- $ -1 \cdot 5 = -5 $

So:
$$
6x - 66 - 3x - 5
$$

Combine:
- $ 6x - 3x = 3x $
- $ -66 - 5 = -71 $

✔ Answer: $ 3x - 71 $

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7.) $ 2(x - 1) - 3(4x - 7) $

Distribute:
- $ 2 \cdot x = 2x $
- $ 2 \cdot (-1) = -2 $
- $ -3 \cdot 4x = -12x $
- $ -3 \cdot (-7) = +21 $

So:
$$
2x - 2 - 12x + 21
$$

Combine:
- $ 2x - 12x = -10x $
- $ -2 + 21 = 19 $

✔ Answer: $ -10x + 19 $

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

Distribute:
- $ 8 \cdot 7x = 56x $
- $ 8 \cdot (-3) = -24 $
- $ -8 \cdot x = -8x $
- $ -8 \cdot 8 = -64 $

So:
$$
56x - 24 - 8x - 64
$$

Combine:
- $ 56x - 8x = 48x $
- $ -24 - 64 = -88 $

✔ Answer: $ 48x - 88 $

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9.) $ 6(4x + 11) + 2(x + 8) $

Distribute:
- $ 6 \cdot 4x = 24x $
- $ 6 \cdot 11 = 66 $
- $ 2 \cdot x = 2x $
- $ 2 \cdot 8 = 16 $

So:
$$
24x + 66 + 2x + 16
$$

Combine:
- $ 24x + 2x = 26x $
- $ 66 + 16 = 82 $

✔ Answer: $ 26x + 82 $

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10.) $ 8(x + 1) + 5(4x - 7) $

Distribute:
- $ 8 \cdot x = 8x $
- $ 8 \cdot 1 = 8 $
- $ 5 \cdot 4x = 20x $
- $ 5 \cdot (-7) = -35 $

So:
$$
8x + 8 + 20x - 35
$$

Combine:
- $ 8x + 20x = 28x $
- $ 8 - 35 = -27 $

✔ Answer: $ 28x - 27 $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1.) | $ 56x - 88 $ |
| 2.) | $ -30x + 84 $ |
| 3.) | $ -16x + 118 $ |
| 4.) | $ 66x + 61 $ |
| 5.) | $ -14x + 85 $ |
| 6.) | $ 3x - 71 $ |
| 7.) | $ -10x + 19 $ |
| 8.) | $ 48x - 88 $ |
| 9.) | $ 26x + 82 $ |
| 10.) | $ 28x - 27 $ |

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