Algebra 1 Unit 8 Adding and Subtracting Polynomials Worksheet ... - Free Printable

Let's solve each problem step by step from the worksheet on adding and subtracting polynomials. The key idea is to combine like terms (terms with the same variable and exponent).

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1. $(x^2 - 3x + 4) + (2x^2 - 7x - 8)$

Step 1: Remove parentheses (since it's addition, signs stay the same):
$$
x^2 - 3x + 4 + 2x^2 - 7x - 8
$$

Step 2: Combine like terms:
- $x^2 + 2x^2 = 3x^2$
- $-3x - 7x = -10x$
- $4 - 8 = -4$

✔ Answer: $3x^2 - 10x - 4$

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

Step 1: Distribute the negative sign to the second polynomial:
$$
-x^2 + 5x - 3 - 3x^2 - x + 2
$$

Step 2: Combine like terms:
- $-x^2 - 3x^2 = -4x^2$
- $5x - x = 4x$
- $-3 + 2 = -1$

✔ Answer: $-4x^2 + 4x - 1$

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3. $(-7x^2 + x + 9) - (x^2 - 7x + 6)$

Step 1: Distribute the negative:
$$
-7x^2 + x + 9 - x^2 + 7x - 6
$$

Step 2: Combine like terms:
- $-7x^2 - x^2 = -8x^2$
- $x + 7x = 8x$
- $9 - 6 = 3$

✔ Answer: $-8x^2 + 8x + 3$

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4. $(6x^2 - 3x - 2) + (-5x^2 - 7x - 1)$

Step 1: Remove parentheses (addition):
$$
6x^2 - 3x - 2 - 5x^2 - 7x - 1
$$

Step 2: Combine like terms:
- $6x^2 - 5x^2 = x^2$
- $-3x - 7x = -10x$
- $-2 - 1 = -3$

✔ Answer: $x^2 - 10x - 3$

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5. $(4x^2 - 3x - 11) + (x - 6 - 4x^2)$

Step 1: Remove parentheses:
$$
4x^2 - 3x - 11 + x - 6 - 4x^2
$$

Step 2: Combine like terms:
- $4x^2 - 4x^2 = 0$
- $-3x + x = -2x$
- $-11 - 6 = -17$

✔ Answer: $-2x - 17$

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6. $(2x - 5 + 4x^2) - (5 - 7x^2 - 3x)$

Step 1: Rewrite in standard form and distribute the negative:
$$
4x^2 + 2x - 5 - 5 + 7x^2 + 3x
$$

Step 2: Combine like terms:
- $4x^2 + 7x^2 = 11x^2$
- $2x + 3x = 5x$
- $-5 - 5 = -10$

✔ Answer: $11x^2 + 5x - 10$

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7. $(6c^2 + 3c + 9) - (3c - 5)$

Step 1: Distribute the negative:
$$
6c^2 + 3c + 9 - 3c + 5
$$

Step 2: Combine like terms:
- $3c - 3c = 0$
- $9 + 5 = 14$

✔ Answer: $6c^2 + 14$

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8. $(9p^3 - 6p^2 + 3 - 11p) + (7p^3 - 3p^2 + 4)$

Step 1: Remove parentheses:
$$
9p^3 - 6p^2 + 3 - 11p + 7p^3 - 3p^2 + 4
$$

Step 2: Combine like terms:
- $9p^3 + 7p^3 = 16p^3$
- $-6p^2 - 3p^2 = -9p^2$
- $-11p$ (no other $p$ term)
- $3 + 4 = 7$

✔ Answer: $16p^3 - 9p^2 - 11p + 7$

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9. $(-n^2 + 2n) - (2n^3 - n^2 + n + 12)$

Step 1: Distribute the negative:
$$
-n^2 + 2n - 2n^3 + n^2 - n - 12
$$

Step 2: Combine like terms:
- $-2n^3$ (only one)
- $-n^2 + n^2 = 0$
- $2n - n = n$
- $-12$

✔ Answer: $-2n^3 + n - 12$

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10. $(x^2 + 4x - 4) + (5x^2 - 8x + 2)$

Step 1: Remove parentheses:
$$
x^2 + 4x - 4 + 5x^2 - 8x + 2
$$

Step 2: Combine like terms:
- $x^2 + 5x^2 = 6x^2$
- $4x - 8x = -4x$
- $-4 + 2 = -2$

✔ Answer: $6x^2 - 4x - 2$

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $3x^2 - 10x - 4$ |
| 2 | $-4x^2 + 4x - 1$ |
| 3 | $-8x^2 + 8x + 3$ |
| 4 | $x^2 - 10x - 3$ |
| 5 | $-2x - 17$ |
| 6 | $11x^2 + 5x - 10$ |
| 7 | $6c^2 + 14$ |
| 8 | $16p^3 - 9p^2 - 11p + 7$ |
| 9 | $-2n^3 + n - 12$ |
| 10 | $6x^2 - 4x - 2$ |

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