Practice simplifying algebraic expressions with this tiered worksheet designed for progressive learning.

Absolutely! Let’s solve each problem by combining like terms. Like terms are terms that have the same variable(s) raised to the same power(s). We add or subtract their coefficients.

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## ✔ Easy Level

1. `3x + 2y + 5x`

- Like terms: `3x` and `5x` (both have `x`)
- Combine: `3x + 5x = 8x`
- `2y` has no other like term → stays as is
✔ Answer: `8x + 2y`

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2. `7p - 3q - 2p + 5q`

- Like terms for `p`: `7p - 2p = 5p`
- Like terms for `q`: `-3q + 5q = 2q`
✔ Answer: `5p + 2q`

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3. `4a - 2b + 2a + 3b`

- `a` terms: `4a + 2a = 6a`
- `b` terms: `-2b + 3b = b`
✔ Answer: `6a + b`

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4. `6x + 2y + 3x - 4y`

- `x` terms: `6x + 3x = 9x`
- `y` terms: `2y - 4y = -2y`
✔ Answer: `9x - 2y`

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## ✔ Medium Level

1. `3a + 2b - 4a + 5b`

- `a` terms: `3a - 4a = -a`
- `b` terms: `2b + 5b = 7b`
✔ Answer: `-a + 7b` (or `7b - a`)

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2. `4x + 2y + 3x - y`

- `x` terms: `4x + 3x = 7x`
- `y` terms: `2y - y = y`
✔ Answer: `7x + y`

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3. `5m - 2n + 3m + 2n`

- `m` terms: `5m + 3m = 8m`
- `n` terms: `-2n + 2n = 0` → cancels out
✔ Answer: `8m`

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4. `8c - 2d + 4c - 3d`

- `c` terms: `8c + 4c = 12c`
- `d` terms: `-2d - 3d = -5d`
✔ Answer: `12c - 5d`

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## ✔ Hard Level

1. `2x + 3y - 4x + 5y - 3z`

- `x` terms: `2x - 4x = -2x`
- `y` terms: `3y + 5y = 8y`
- `z` term: `-3z` (no other `z` term)
✔ Answer: `-2x + 8y - 3z`

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2. `5a² + 2b - 3a² - 6b`

- `a²` terms: `5a² - 3a² = 2a²`
- `b` terms: `2b - 6b = -4b`
✔ Answer: `2a² - 4b`

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3. `4p³ + 3q - 2p³ + 5q`

- `p³` terms: `4p³ - 2p³ = 2p³`
- `q` terms: `3q + 5q = 8q`
✔ Answer: `2p³ + 8q`

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4. `6ab² - 3bc² + 5ab² + 4bc²`

- `ab²` terms: `6ab² + 5ab² = 11ab²`
- `bc²` terms: `-3bc² + 4bc² = bc²`
✔ Answer: `11ab² + bc²`

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## 📌 Final Answers Summary:

Easy:

1. `8x + 2y`
2. `5p + 2q`
3. `6a + b`
4. `9x - 2y`

Medium:

1. `-a + 7b`
2. `7x + y`
3. `8m`
4. `12c - 5d`

Hard:

1. `-2x + 8y - 3z`
2. `2a² - 4b`
3. `2p³ + 8q`
4. `11ab² + bc²`

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