Simplifying Algebraic Expressions worksheet with 32 practice problems for students.

Let's solve each of these algebraic expressions step by step, simplifying them using distribution, combining like terms, and basic algebraic rules.

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1) $ 3(x + 9) $

Distribute the 3:
$$
3x + 27
$$

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2) $ (-6)(8x - 4) $

Distribute $-6$:
$$
-48x + 24
$$

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3) $ 7x + 3 - 3x $

Combine like terms:
$$
(7x - 3x) + 3 = 4x + 3
$$

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4) $ -2 - x^2 - 6x^2 $

Combine like terms:
$$
-2 - (x^2 + 6x^2) = -2 - 7x^2 \quad \text{or} \quad -7x^2 - 2
$$

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5) $ 3 + 10x^2 + 2 $

Combine constants:
$$
10x^2 + 5
$$

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6) $ 8x^2 + 6x + 7x^2 $

Combine like terms:
$$
(8x^2 + 7x^2) + 6x = 15x^2 + 6x
$$

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7) $ 5x^2 - 12x^2 + 8x $

Combine like terms:
$$
(-7x^2) + 8x = -7x^2 + 8x
$$

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8) $ 2x^2 - 2x - x $

Combine like terms:
$$
2x^2 - 3x
$$

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9) $ 4x + 6(2 - 5x) $

Distribute 6:
$$
4x + 12 - 30x = (4x - 30x) + 12 = -26x + 12
$$

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10) $ 10x + 8(10x - 6) $

Distribute 8:
$$
10x + 80x - 48 = 90x - 48
$$

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11) $ 9(-2x - 6) - 5 $

Distribute 9:
$$
-18x - 54 - 5 = -18x - 59
$$

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12) $ 2x^2 + (-8x) $

Simplify:
$$
2x^2 - 8x
$$

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13) $ x - 3 + 5 - 3x $

Combine like terms:
$$
(x - 3x) + (-3 + 5) = -2x + 2
$$

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14) $ 2 - 3x + 12 - 2x $

Combine:
$$
(2 + 12) + (-3x - 2x) = 14 - 5x
$$

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15) $ 32x - 4 + 23 + 2x $

Combine:
$$
(32x + 2x) + (-4 + 23) = 34x + 19
$$

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16) $ (-6)(8x - 4) + 10x $

First distribute $-6$:
$$
-48x + 24 + 10x = (-48x + 10x) + 24 = -38x + 24
$$

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17) $ 14x - 5(5 - 8x) $

Distribute $-5$:
$$
14x - 25 + 40x = (14x + 40x) - 25 = 54x - 25
$$

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18) $ 23x + 4(9x + 3) + 12 $

Distribute 4:
$$
23x + 36x + 12 + 12 = (23x + 36x) + (12 + 12) = 59x + 24
$$

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19) $ 3(-7x + 5) + 20x $

Distribute 3:
$$
-21x + 15 + 20x = (-21x + 20x) + 15 = -x + 15
$$

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20) $ 12x - 3x(x + 9) $

Distribute $-3x$:
$$
12x - 3x^2 - 27x = (-3x^2) + (12x - 27x) = -3x^2 - 15x
$$

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21) $ 7x + 5x(3 - 3x) $

Distribute $5x$:
$$
7x + 15x - 15x^2 = (7x + 15x) - 15x^2 = 22x - 15x^2
\quad \text{or} \quad -15x^2 + 22x
$$

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22) $ 5x(-8x + 12) + 14x $

Distribute $5x$:
$$
-40x^2 + 60x + 14x = -40x^2 + 74x
$$

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23) $ 40x + 12 + 2x^2 $

Rearrange in standard form:
$$
2x^2 + 40x + 12
$$

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24) $ 5x(x - 3) - 10 $

Distribute $5x$:
$$
5x^2 - 15x - 10
$$

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25) $ 8x - 7 + 8x + 2x^2 $

Combine like terms:
$$
2x^2 + (8x + 8x) - 7 = 2x^2 + 16x - 7
$$

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26) $ 2x^2 - 5x - 7x $

Combine like terms:
$$
2x^2 - 12x
$$

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27) $ 7x - 3x^2 - 5x^2 - 3 $

Combine like terms:
$$
(-3x^2 - 5x^2) + 7x - 3 = -8x^2 + 7x - 3
$$

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28) $ 4 + x^2 - 6x^2 - 12x $

Combine:
$$
(4) + (x^2 - 6x^2) - 12x = 4 - 5x^2 - 12x
\quad \text{or} \quad -5x^2 - 12x + 4
$$

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29) $ 12x + 8x^2 + 2x + 20 $

Combine like terms:
$$
8x^2 + (12x + 2x) + 20 = 8x^2 + 14x + 20
$$

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30) $ 2x^2 + 6x + 3x^2 $

Combine:
$$
(2x^2 + 3x^2) + 6x = 5x^2 + 6x
$$

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31) $ 23 + 15x^2 + 8x - 4x^2 $

Combine:
$$
(15x^2 - 4x^2) + 8x + 23 = 11x^2 + 8x + 23
$$

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32) $ 8x - 12x - x^2 + 13 $

Combine:
$$
(-4x) - x^2 + 13 = -x^2 - 4x + 13
$$

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✔ Final Answers:

| Problem | Simplified Expression |
|--------|------------------------|
| 1 | $ 3x + 27 $ |
| 2 | $ -48x + 24 $ |
| 3 | $ 4x + 3 $ |
| 4 | $ -7x^2 - 2 $ |
| 5 | $ 10x^2 + 5 $ |
| 6 | $ 15x^2 + 6x $ |
| 7 | $ -7x^2 + 8x $ |
| 8 | $ 2x^2 - 3x $ |
| 9 | $ -26x + 12 $ |
| 10 | $ 90x - 48 $ |
| 11 | $ -18x - 59 $ |
| 12 | $ 2x^2 - 8x $ |
| 13 | $ -2x + 2 $ |
| 14 | $ 14 - 5x $ |
| 15 | $ 34x + 19 $ |
| 16 | $ -38x + 24 $ |
| 17 | $ 54x - 25 $ |
| 18 | $ 59x + 24 $ |
| 19 | $ -x + 15 $ |
| 20 | $ -3x^2 - 15x $ |
| 21 | $ -15x^2 + 22x $ |
| 22 | $ -40x^2 + 74x $ |
| 23 | $ 2x^2 + 40x + 12 $ |
| 24 | $ 5x^2 - 15x - 10 $ |
| 25 | $ 2x^2 + 16x - 7 $ |
| 26 | $ 2x^2 - 12x $ |
| 27 | $ -8x^2 + 7x - 3 $ |
| 28 | $ -5x^2 - 12x + 4 $ |
| 29 | $ 8x^2 + 14x + 20 $ |
| 30 | $ 5x^2 + 6x $ |
| 31 | $ 11x^2 + 8x + 23 $ |
| 32 | $ -x^2 - 4x + 13 $ |

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✔ Key Concepts Used:
- Distributive Property: $ a(b + c) = ab + ac $
- Combining Like Terms: Terms with same variables and exponents
- Order of Operations: Always simplify inside parentheses first, then multiply/divide, then add/subtract
- Standard Form: Writing polynomials in descending powers of $x$

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