Worksheet for practicing addition and subtraction of polynomials with 12 problems.

It looks like you've uploaded a worksheet titled "Adding and Subtracting Polynomials 'Misty Lanes' (c)", which includes 12 polynomial addition and subtraction problems. The goal is to simplify each expression by combining like terms.

Below is the solution for each problem, along with a brief explanation of how to solve them.

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🔷 Instructions Recap:

- Combine like terms (terms with the same variable and exponent).
- Pay attention to signs, especially when subtracting polynomials.
- Distribute the negative sign if needed.

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✔ Solutions with Explanations

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#### 1. $(3x^2 + 5x^2) + (4x^2 - 3x + 6x^2)$

Step-by-step:
- Combine $3x^2 + 5x^2 = 8x^2$
- Combine $4x^2 + 6x^2 = 10x^2$
- So total: $8x^2 + 10x^2 = 18x^2$
- Add $-3x$ → final: $18x^2 - 3x$

✔ Answer: $18x^2 - 3x$

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#### 2. $(7 + 8x^2) - (2x^2 + 4 + 2x^2)$

Step-by-step:
- Simplify inside parentheses: $2x^2 + 2x^2 = 4x^2$, so second group is $4x^2 + 4$
- Now: $7 + 8x^2 - (4x^2 + 4)$
- Distribute negative: $7 + 8x^2 - 4x^2 - 4$
- Combine: $(8x^2 - 4x^2) + (7 - 4) = 4x^2 + 3$

✔ Answer: $4x^2 + 3$

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#### 3. $(6x^2 - 7) - (5x^2 + 2 + x^2)$

Step-by-step:
- Simplify right side: $5x^2 + x^2 = 6x^2$, so $6x^2 + 2$
- Now: $6x^2 - 7 - (6x^2 + 2)$
- Distribute negative: $6x^2 - 7 - 6x^2 - 2$
- Combine: $(6x^2 - 6x^2) + (-7 - 2) = 0 - 9 = -9$

✔ Answer: $-9$

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#### 4. $(4x + 4 + 3x^2) - (2x^2 + 5 + 5x^2)$

Step-by-step:
- Right side: $2x^2 + 5x^2 = 7x^2$, so $7x^2 + 5$
- Left side: $3x^2 + 4x + 4$
- Subtract: $3x^2 + 4x + 4 - 7x^2 - 5$
- Combine: $(3x^2 - 7x^2) + 4x + (4 - 5) = -4x^2 + 4x - 1$

✔ Answer: $-4x^2 + 4x - 1$

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#### 5. $(6x + 4x^2) + (2x + 3x^2 - 8)$

Step-by-step:
- Group like terms:
- $4x^2 + 3x^2 = 7x^2$
- $6x + 2x = 8x$
- Constant: $-8$
- Result: $7x^2 + 8x - 8$

✔ Answer: $7x^2 + 8x - 8$

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#### 6. $(2 + 4x^2 + 5x^2) + (2x + 4x^2 - 7)$

Step-by-step:
- First group: $4x^2 + 5x^2 = 9x^2$, so $9x^2 + 2$
- Second group: $4x^2 + 2x - 7$
- Add: $9x^2 + 2 + 4x^2 + 2x - 7$
- Combine: $(9x^2 + 4x^2) + 2x + (2 - 7) = 13x^2 + 2x - 5$

✔ Answer: $13x^2 + 2x - 5$

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#### 7. $(3x^2 + 5x^2) - (5x^2 + 2x^2)$

Step-by-step:
- Left: $3x^2 + 5x^2 = 8x^2$
- Right: $5x^2 + 2x^2 = 7x^2$
- Subtract: $8x^2 - 7x^2 = x^2$

✔ Answer: $x^2$

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#### 8. $(2x - 5x^2 - 7) - (2x + 5x^2 + 3x^2)$

Step-by-step:
- Right side: $5x^2 + 3x^2 = 8x^2$, so $2x + 8x^2$
- Left: $-5x^2 + 2x - 7$
- Subtract: $-5x^2 + 2x - 7 - (8x^2 + 2x)$
- Distribute: $-5x^2 + 2x - 7 - 8x^2 - 2x$
- Combine: $(-5x^2 - 8x^2) + (2x - 2x) - 7 = -13x^2 + 0x - 7$

✔ Answer: $-13x^2 - 7$

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#### 9. $(5x^2 + 3x^2 - 4) - (3x^2 + 4x^2 + 6)$

Step-by-step:
- Left: $5x^2 + 3x^2 = 8x^2$, so $8x^2 - 4$
- Right: $3x^2 + 4x^2 = 7x^2$, so $7x^2 + 6$
- Subtract: $8x^2 - 4 - 7x^2 - 6$
- Combine: $(8x^2 - 7x^2) + (-4 - 6) = x^2 - 10$

✔ Answer: $x^2 - 10$

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#### 10. $(2x^2 + 4 - 4x^2) + (x^2 - 3x^2 + 5)$

Step-by-step:
- Left: $2x^2 - 4x^2 = -2x^2$, so $-2x^2 + 4$
- Right: $x^2 - 3x^2 = -2x^2$, so $-2x^2 + 5$
- Add: $-2x^2 + 4 - 2x^2 + 5 = (-2x^2 - 2x^2) + (4 + 5) = -4x^2 + 9$

✔ Answer: $-4x^2 + 9$

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#### 11. $(4x^2 + 4x^2) + (2x^2 + 5x^2)$

Step-by-step:
- $4x^2 + 4x^2 = 8x^2$
- $2x^2 + 5x^2 = 7x^2$
- Total: $8x^2 + 7x^2 = 15x^2$

✔ Answer: $15x^2$

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#### 12. $(-2 + 4x^2 + 5x^2) + (2x^2 + 4x^2 - 5)$

Step-by-step:
- Left: $4x^2 + 5x^2 = 9x^2$, so $9x^2 - 2$
- Right: $2x^2 + 4x^2 = 6x^2$, so $6x^2 - 5$
- Add: $9x^2 - 2 + 6x^2 - 5 = (9x^2 + 6x^2) + (-2 - 5) = 15x^2 - 7$

✔ Answer: $15x^2 - 7$

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📌 Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $18x^2 - 3x$ |
| 2 | $4x^2 + 3$ |
| 3 | $-9$ |
| 4 | $-4x^2 + 4x - 1$ |
| 5 | $7x^2 + 8x - 8$ |
| 6 | $13x^2 + 2x - 5$ |
| 7 | $x^2$ |
| 8 | $-13x^2 - 7$ |
| 9 | $x^2 - 10$ |
| 10 | $-4x^2 + 9$ |
| 11 | $15x^2$ |
| 12 | $15x^2 - 7$ |

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✔ Tips for Success:

- Always distribute the negative sign when subtracting polynomials.
- Combine like terms only (same variables and exponents).
- Keep track of signs — especially when subtracting.
- Double-check your arithmetic.

Let me know if you'd like this in a printable format or need help with graphing or other algebra topics!