Simplifying Algebraic Expressions - Worksheets and Quiz (Combine Like Terms) - Free Printable

Sure! Let’s simplify each expression step by step. We’ll use the distributive property (a(b + c) = ab + ac), combine like terms, and follow order of operations.

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🔹 Left Column:

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1. `2t(3t + 2) + 5t`

Distribute `2t`:
→ `2t * 3t = 6t²`
→ `2t * 2 = 4t`
So: `6t² + 4t + 5t`

Combine like terms (`4t + 5t = 9t`):

✔ Final Answer: `6t² + 9t`

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2. `-m(2m + 3) - 8`

Distribute `-m`:
→ `-m * 2m = -2m²`
→ `-m * 3 = -3m`
So: `-2m² - 3m - 8`

No like terms to combine.

✔ Final Answer: `-2m² - 3m - 8`

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3. `w(-3w + 5) - 5t`

Distribute `w`:
→ `w * -3w = -3w²`
→ `w * 5 = 5w`
So: `-3w² + 5w - 5t`

No like terms (different variables).

✔ Final Answer: `-3w² + 5w - 5t`

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4. `-2z(-4p + 6z) + 8p`

Distribute `-2z`:
→ `-2z * -4p = 8zp` (or `8pz`)
→ `-2z * 6z = -12z²`
So: `8pz - 12z² + 8p`

We can write terms in standard order (alphabetical or descending powers). Since no like terms, we just rearrange for clarity.

✔ Final Answer: `-12z² + 8pz + 8p`

*(Note: `8pz` is same as `8zp`, but typically written as `8pz`)*

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5. `10p + 5(6 + 7p)`

Distribute `5`:
→ `5 * 6 = 30`
→ `5 * 7p = 35p`
So: `10p + 30 + 35p`

Combine like terms (`10p + 35p = 45p`):

✔ Final Answer: `45p + 30`

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🔹 Right Column:

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6. `10k + 2k(-8k - 5)`

Distribute `2k`:
→ `2k * -8k = -16k²`
→ `2k * -5 = -10k`
So: `10k - 16k² - 10k`

Combine like terms (`10k - 10k = 0`):

✔ Final Answer: `-16k²`

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7. `3x - 3x(-7x + 9y - 2)`

Distribute `-3x` (note the minus sign!):
→ `-3x * -7x = 21x²`
→ `-3x * 9y = -27xy`
→ `-3x * -2 = 6x`
So: `3x + 21x² - 27xy + 6x`

Combine like terms (`3x + 6x = 9x`):

✔ Final Answer: `21x² - 27xy + 9x`

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8. `-5w(-5 - 4y - 2w) - 10w²`

First, distribute `-5w`:
→ `-5w * -5 = 25w`
→ `-5w * -4y = 20wy`
→ `-5w * -2w = 10w²`
So: `25w + 20wy + 10w² - 10w²`

Now combine like terms: `10w² - 10w² = 0`

✔ Final Answer: `25w + 20wy`

*(You can also write as `20wy + 25w` — same thing)*

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9. `-4(7n - 9p - 3) + 4p`

Distribute `-4`:
→ `-4 * 7n = -28n`
→ `-4 * -9p = 36p`
→ `-4 * -3 = 12`
So: `-28n + 36p + 12 + 4p`

Combine like terms (`36p + 4p = 40p`):

✔ Final Answer: `-28n + 40p + 12`

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10. `5t² - 4t(2t + 4g)`

Distribute `-4t`:
→ `-4t * 2t = -8t²`
→ `-4t * 4g = -16tg`
So: `5t² - 8t² - 16tg`

Combine like terms (`5t² - 8t² = -3t²`):

✔ Final Answer: `-3t² - 16tg`

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## ✔ Final Simplified Expressions:

Left Column:
1. `6t² + 9t`
2. `-2m² - 3m - 8`
3. `-3w² + 5w - 5t`
4. `-12z² + 8pz + 8p`
5. `45p + 30`

Right Column:
6. `-16k²`
7. `21x² - 27xy + 9x`
8. `25w + 20wy`
9. `-28n + 40p + 12`
10. `-3t² - 16tg`

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Let me know if you’d like to see any step explained further! 😊