Pre-Algebra Worksheets | Monomials and Polynomials Worksheets - Free Printable

Let's solve each of the polynomial addition and subtraction problems step by step. We'll combine like terms (terms with the same variable and exponent) to simplify each expression.

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1) $(q^2 - 8q^2 - 7) + (3q^2 + 4 - 5q^2) + (9q^2 - 6q - 2)$

First, let's rewrite each part clearly:

- First: $q^2 - 8q^2 - 7 = (-7q^2 - 7)$
- Second: $3q^2 + 4 - 5q^2 = (-2q^2 + 4)$
- Third: $9q^2 - 6q - 2$

Now add all together:

$$
(-7q^2 - 7) + (-2q^2 + 4) + (9q^2 - 6q - 2)
$$

Combine like terms:

- $q^2$: $-7 - 2 + 9 = 0$
- $q$: $-6q$
- Constant: $-7 + 4 - 2 = -5$

✔ Answer: $-6q - 5$

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2) $(6c - 4c^2 - 3) - (9c + 5c^2 - 8c^2)$

Simplify inside parentheses first:

- Second group: $9c + 5c^2 - 8c^2 = 9c - 3c^2$

Now subtract:

$$
(6c - 4c^2 - 3) - (9c - 3c^2)
= 6c - 4c^2 - 3 - 9c + 3c^2
$$

Combine like terms:

- $c^2$: $-4c^2 + 3c^2 = -c^2$
- $c$: $6c - 9c = -3c$
- Constant: $-3$

✔ Answer: $-c^2 - 3c - 3$

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3) $(8q^3 - 3q^2 + 2q) - (4q^2 - 5q) + (7q - 9q^2 + 6q^3)$

Distribute the minus sign:

$$
8q^3 - 3q^2 + 2q - 4q^2 + 5q + 7q - 9q^2 + 6q^3
$$

Now combine like terms:

- $q^3$: $8q^3 + 6q^3 = 14q^3$
- $q^2$: $-3q^2 - 4q^2 - 9q^2 = -16q^2$
- $q$: $2q + 5q + 7q = 14q$

✔ Answer: $14q^3 - 16q^2 + 14q$

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4) $(6d^2 - 4) + (9 + 8d^2 - 5d^2)$

Simplify second group: $9 + 8d^2 - 5d^2 = 9 + 3d^2$

Now add:

$$
6d^2 - 4 + 3d^2 + 9 = (6d^2 + 3d^2) + (-4 + 9) = 9d^2 + 5
$$

✔ Answer: $9d^2 + 5$

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5) $(3z^2 + 5) + (4z^2 + 8 - 9z^2) + (6z^2 + 7z - 2)$

Simplify second group: $4z^2 + 8 - 9z^2 = -5z^2 + 8$

Now add all:

$$
3z^2 + 5 - 5z^2 + 8 + 6z^2 + 7z - 2
$$

Combine:

- $z^2$: $3 - 5 + 6 = 4z^2$
- $z$: $7z$
- Constant: $5 + 8 - 2 = 11$

✔ Answer: $4z^2 + 7z + 11$

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6) $(7p^2 - 4p^2 + 3p) - (5p^2 + 6p^3) + (9p^2 - 8p^3 + 2p^3)$

First simplify each group:

- First: $7p^2 - 4p^2 + 3p = 3p^2 + 3p$
- Second: $5p^2 + 6p^3$
- Third: $9p^2 - 8p^3 + 2p^3 = 9p^2 - 6p^3$

Now compute:

$$
(3p^2 + 3p) - (5p^2 + 6p^3) + (9p^2 - 6p^3)
= 3p^2 + 3p - 5p^2 - 6p^3 + 9p^2 - 6p^3
$$

Combine:

- $p^3$: $-6p^3 - 6p^3 = -12p^3$
- $p^2$: $3p^2 - 5p^2 + 9p^2 = 7p^2$
- $p$: $3p$

✔ Answer: $-12p^3 + 7p^2 + 3p$

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7) $(8y^6 - 2) - (9y^6 + 5 + 3y^2)$

Distribute the minus:

$$
8y^6 - 2 - 9y^6 - 5 - 3y^2
$$

Combine:

- $y^6$: $8 - 9 = -y^6$
- $y^2$: $-3y^2$
- Constant: $-2 - 5 = -7$

✔ Answer: $-y^6 - 3y^2 - 7$

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8) $(7z^2 + 5z^2 - 4z^3) - (8z^2 + 6) - (9z^2 + 3z^2)$

Wait — double-check: in the first term: $7z^2 + 5z^2 - 4z^3 = 12z^2 - 4z^3$

Second: $8z^2 + 6$

Third: $9z^2 + 3z^2 = 12z^2$

Now:

$$
(12z^2 - 4z^3) - (8z^2 + 6) - (12z^2)
= 12z^2 - 4z^3 - 8z^2 - 6 - 12z^2
$$

Combine:

- $z^3$: $-4z^3$
- $z^2$: $12 - 8 - 12 = -8z^2$
- Constant: $-6$

✔ Answer: $-4z^3 - 8z^2 - 6$

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9) $(2p - 8p^2) - (4p + 6p^2 - 5)$

Distribute the minus:

$$
2p - 8p^2 - 4p - 6p^2 + 5
$$

Combine:

- $p^2$: $-8p^2 - 6p^2 = -14p^2$
- $p$: $2p - 4p = -2p$
- Constant: $+5$

✔ Answer: $-14p^2 - 2p + 5$

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10) $(6x^3 - 5x^2) - (2x^2 - 4x + 9x^3)$

Distribute the minus:

$$
6x^3 - 5x^2 - 2x^2 + 4x - 9x^3
$$

Combine:

- $x^3$: $6x^3 - 9x^3 = -3x^3$
- $x^2$: $-5x^2 - 2x^2 = -7x^2$
- $x$: $+4x$

✔ Answer: $-3x^3 - 7x^2 + 4x$

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✔ Final Answers:

1) $-6q - 5$
2) $-c^2 - 3c - 3$
3) $14q^3 - 16q^2 + 14q$
4) $9d^2 + 5$
5) $4z^2 + 7z + 11$
6) $-12p^3 + 7p^2 + 3p$
7) $-y^6 - 3y^2 - 7$
8) $-4z^3 - 8z^2 - 6$
9) $-14p^2 - 2p + 5$
10) $-3x^3 - 7x^2 + 4x$

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