Simplify Polynomials worksheet - Free Printable

Let's simplify each polynomial expression step by step. We will combine like terms and write the answers in decreasing degree order and alphabetical order for variables, as instructed.

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1. $-7 + 4 + 7x - x$

Combine constants:
$-7 + 4 = -3$

Combine $x$-terms:
$7x - x = 6x$

So, result:
$$
6x - 3
$$

✔ Answer: `6x - 3`

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2. $5x - 7 + 5 - 2x$

Combine constants:
$-7 + 5 = -2$

Combine $x$-terms:
$5x - 2x = 3x$

So, result:
$$
3x - 2
$$

✔ Answer: `3x - 2`

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3. $(2x - 1) - (5 - 3x)$

Distribute the negative sign:
$2x - 1 - 5 + 3x$

Combine like terms:
$2x + 3x = 5x$
$-1 - 5 = -6$

Result:
$$
5x - 6
$$

✔ Answer: `5x - 6`

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4. $(3x^2 - 9x - 1) + (4x^2 + 6x + 8)$

Add like terms:

- $x^2$: $3x^2 + 4x^2 = 7x^2$
- $x$: $-9x + 6x = -3x$
- Constants: $-1 + 8 = 7$

Result:
$$
7x^2 - 3x + 7
$$

✔ Answer: `7x^2 - 3x + 7`

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

Combine like terms:

- $x$-terms: $-2x + 4x = 2x$
- Constants: $-3 + 5 = 2$

Result:
$$
2x + 2
$$

✔ Answer: `2x + 2`

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

Distribute the negative sign:
$9x^2 - 3x - 7 + 6x^2 + 6x - 6$

Now combine:

- $x^2$: $9x^2 + 6x^2 = 15x^2$
- $x$: $-3x + 6x = 3x$
- Constants: $-7 - 6 = -13$

Result:
$$
15x^2 + 3x - 13
$$

✔ Answer: `15x^2 + 3x - 13`

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7. $(4m^2 - 3m) - (2m^2 - 5)$

Distribute the negative sign:
$4m^2 - 3m - 2m^2 + 5$

Combine:

- $m^2$: $4m^2 - 2m^2 = 2m^2$
- $m$: $-3m$
- Constant: $+5$

Result:
$$
2m^2 - 3m + 5
$$

✔ Answer: `2m^2 - 3m + 5`

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8. $(2a - 7b + c) + (-6a + 3b + 4c)$

Combine like terms:

- $a$: $2a - 6a = -4a$
- $b$: $-7b + 3b = -4b$
- $c$: $c + 4c = 5c$

Now arrange in alphabetical order:
$a$, then $b$, then $c$

Result:
$$
-4a - 4b + 5c
$$

✔ Answer: `-4a - 4b + 5c`

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✔ Final Answers (in table format):

| Expression | Simplified |
|-----------|------------|
| $-7 + 4 + 7x - x$ | `6x - 3` |
| $5x - 7 + 5 - 2x$ | `3x - 2` |
| $(2x - 1) - (5 - 3x)$ | `5x - 6` |
| $(3x^2 - 9x - 1) + (4x^2 + 6x + 8)$ | `7x^2 - 3x + 7` |
| $(-2x - 3) + (5 + 4x)$ | `2x + 2` |
| $(9x^2 - 3x - 7) - (-6x^2 - 6x + 6)$ | `15x^2 + 3x - 13` |
| $(4m^2 - 3m) - (2m^2 - 5)$ | `2m^2 - 3m + 5` |
| $(2a - 7b + c) + (-6a + 3b + 4c)$ | `-4a - 4b + 5c` |

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