Simplifying Expressions Worksheets - Math Monks - Free Printable

Sure! Let’s simplify each expression one by one by combining like terms. Like terms are terms that have the same variable raised to the same power (or are constants).

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1. `10x + 7 - 5x`

- Combine the x-terms: `10x - 5x = 5x`
- Constant: `+7`

✔ Answer: `5x + 7`

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2. `10y⁴ - 8y³ - 8y² + 16 - 4 + y`

- Group like terms:
- `y⁴`: only `10y⁴`
- `y³`: only `-8y³`
- `y²`: only `-8y²`
- `y`: only `+y`
- Constants: `16 - 4 = 12`

✔ Answer: `10y⁴ - 8y³ - 8y² + y + 12`

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3. `6s - 8s + 4 + 6s`

- Combine s-terms: `6s - 8s + 6s = (6 - 8 + 6)s = 4s`
- Constant: `+4`

✔ Answer: `4s + 4`

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4. `v - 3v + 6 + 8 - 3v²`

- Group like terms:
- `v` terms: `v - 3v = -2v`
- Constants: `6 + 8 = 14`
- `v²` term: `-3v²`

✔ Answer: `-3v² - 2v + 14`

*(Note: Usually we write highest degree first)*

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5. `10a + 8 + 3 - a`

- Combine a-terms: `10a - a = 9a`
- Constants: `8 + 3 = 11`

✔ Answer: `9a + 11`

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6. `3x + 9 + 4x - 5`

- Combine x-terms: `3x + 4x = 7x`
- Constants: `9 - 5 = 4`

✔ Answer: `7x + 4`

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7. `2 + x + 4 - x + 1`

- x-terms: `x - x = 0` → they cancel out
- Constants: `2 + 4 + 1 = 7`

✔ Answer: `7`

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8. `12n - 8 - 2n + 10 - 4`

- n-terms: `12n - 2n = 10n`
- Constants: `-8 + 10 - 4 = -2`

✔ Answer: `10n - 2`

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9. `8d - 4 - 2d + 5`

- d-terms: `8d - 2d = 6d`
- Constants: `-4 + 5 = 1`

✔ Answer: `6d + 1`

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10. `8y + 5 + 3 + 9 - y - 1`

- y-terms: `8y - y = 7y`
- Constants: `5 + 3 + 9 - 1 = 16`

✔ Answer: `7y + 16`

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11. `-3b - b² - 2b²`

- b² terms: `-b² - 2b² = -3b²`
- b term: `-3b`

✔ Answer: `-3b² - 3b`

*(Write higher degree first)*

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12. `u² + 5u + u²`

- u² terms: `u² + u² = 2u²`
- u term: `+5u`

✔ Answer: `2u² + 5u`

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## ✔ Final Answers:

1. `5x + 7`
2. `10y⁴ - 8y³ - 8y² + y + 12`
3. `4s + 4`
4. `-3v² - 2v + 14`
5. `9a + 11`
6. `7x + 4`
7. `7`
8. `10n - 2`
9. `6d + 1`
10. `7y + 16`
11. `-3b² - 3b`
12. `2u² + 5u`

Let me know if you want to see step-by-step work for any specific problem!