Simplifying Algebraic Expressions math worksheet with 32 problems for practice.
Math worksheet titled "Simplifying Algebraic Expressions" with 32 problems for students to simplify, including algebraic expressions with variables, constants, and parentheses. The worksheet is from EffortlessMath and includes spaces for name and date.
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Show Answer Key & Explanations
Step-by-step solution for: SOLUTION: Simplifying algebraic expressions worksheet - Studypool
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Show Answer Key & Explanations
Step-by-step solution for: SOLUTION: Simplifying algebraic expressions worksheet - Studypool
Let's solve each of the algebraic expressions step by step. The goal is to simplify each expression by:
- Using the distributive property where needed.
- Combining like terms (terms with the same variable and exponent).
- Simplifying constants.
---
Distribute 3:
$$
3x + 27
$$
---
Distribute -6:
$$
-48x + 24
$$
---
Combine like terms:
$$
(7x - 3x) + 3 = 4x + 3
$$
---
Combine like terms:
$$
-2 - (x^2 + 6x^2) = -2 - 7x^2 = -7x^2 - 2
$$
---
Combine constants:
$$
(3 + 2) + 10x^2 = 5 + 10x^2 = 10x^2 + 5
$$
---
Combine like terms:
$$
(8x^2 + 7x^2) + 6x = 15x^2 + 6x
$$
---
Combine like terms:
$$
(5x^2 - 12x^2) + 8x = -7x^2 + 8x
$$
---
Combine like terms:
$$
2x^2 - (2x + x) = 2x^2 - 3x
$$
---
Distribute 6:
$$
4x + 12 - 30x = (4x - 30x) + 12 = -26x + 12
$$
---
Distribute 8:
$$
10x + 80x - 48 = 90x - 48
$$
---
Distribute 9:
$$
-18x - 54 - 5 = -18x - 59
$$
---
Simplify:
$$
2x^2 - 8x
$$
---
Combine like terms:
$$
(x - 3x) + (-3 + 5) = -2x + 2
$$
---
Combine like terms:
$$
(2 + 12) + (-3x - 2x) = 14 - 5x
$$
---
Combine like terms:
$$
(32x + 2x) + (-4 + 23) = 34x + 19
$$
---
First distribute -6:
$$
-48x + 24 + 10x = (-48x + 10x) + 24 = -38x + 24
$$
---
Distribute -5:
$$
14x - 25 + 40x = (14x + 40x) - 25 = 54x - 25
$$
---
Distribute 4:
$$
23x + 36x + 12 + 12 = (23x + 36x) + (12 + 12) = 59x + 24
$$
---
Distribute 3:
$$
-21x + 15 + 20x = (-21x + 20x) + 15 = -x + 15
$$
---
Distribute -3x:
$$
12x - 3x^2 - 27x = (-3x^2) + (12x - 27x) = -3x^2 - 15x
$$
---
Distribute 5x:
$$
7x + 15x - 15x^2 = (7x + 15x) - 15x^2 = 22x - 15x^2 = -15x^2 + 22x
$$
---
Distribute 5x:
$$
-40x^2 + 60x + 14x = -40x^2 + 74x
$$
---
Rewrite in standard form:
$$
2x^2 + 40x + 12
$$
---
Distribute 5x:
$$
5x^2 - 15x - 10
$$
---
Combine like terms:
$$
2x^2 + (8x + 8x) - 7 = 2x^2 + 16x - 7
$$
---
Combine like terms:
$$
2x^2 - 12x
$$
---
Combine like terms:
$$
(-3x^2 - 5x^2) + 7x - 3 = -8x^2 + 7x - 3
$$
---
Combine like terms:
$$
(4) + (x^2 - 6x^2) - 12x = 4 - 5x^2 - 12x = -5x^2 - 12x + 4
$$
---
Combine like terms:
$$
(12x + 2x) + 8x^2 + 28 = 14x + 8x^2 + 28 = 8x^2 + 14x + 28
$$
---
Combine like terms:
$$
(2x^2 + 3x^2) + 6x = 5x^2 + 6x
$$
---
Combine like terms:
$$
(15x^2 - 4x^2) + 8x + 23 = 11x^2 + 8x + 23
$$
---
Combine like terms:
$$
(8x - 12x) - x^2 + 13 = -4x - x^2 + 13 = -x^2 - 4x + 13
$$
---
## ✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 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 + 28 $ |
| 30 | $ 5x^2 + 6x $ |
| 31 | $ 11x^2 + 8x + 23 $ |
| 32 | $ -x^2 - 4x + 13 $ |
---
Let me know if you'd like this as a printable PDF or need help understanding any specific problem!
- Using the distributive property where needed.
- Combining like terms (terms with the same variable and exponent).
- Simplifying constants.
---
1) $ 3(x + 9) $
Distribute 3:
$$
3x + 27
$$
---
2) $ (-6)(8x - 4) $
Distribute -6:
$$
-48x + 24
$$
---
3) $ 7x + 3 - 3x $
Combine like terms:
$$
(7x - 3x) + 3 = 4x + 3
$$
---
4) $ -2 - x^2 - 6x^2 $
Combine like terms:
$$
-2 - (x^2 + 6x^2) = -2 - 7x^2 = -7x^2 - 2
$$
---
5) $ 3 + 10x^2 + 2 $
Combine constants:
$$
(3 + 2) + 10x^2 = 5 + 10x^2 = 10x^2 + 5
$$
---
6) $ 8x^2 + 6x + 7x^2 $
Combine like terms:
$$
(8x^2 + 7x^2) + 6x = 15x^2 + 6x
$$
---
7) $ 5x^2 - 12x^2 + 8x $
Combine like terms:
$$
(5x^2 - 12x^2) + 8x = -7x^2 + 8x
$$
---
8) $ 2x^2 - 2x - x $
Combine like terms:
$$
2x^2 - (2x + x) = 2x^2 - 3x
$$
---
9) $ 4x + 6(2 - 5x) $
Distribute 6:
$$
4x + 12 - 30x = (4x - 30x) + 12 = -26x + 12
$$
---
10) $ 10x + 8(10x - 6) $
Distribute 8:
$$
10x + 80x - 48 = 90x - 48
$$
---
11) $ 9(-2x - 6) - 5 $
Distribute 9:
$$
-18x - 54 - 5 = -18x - 59
$$
---
12) $ 2x^2 + (-8x) $
Simplify:
$$
2x^2 - 8x
$$
---
13) $ x - 3 + 5 - 3x $
Combine like terms:
$$
(x - 3x) + (-3 + 5) = -2x + 2
$$
---
14) $ 2 - 3x + 12 - 2x $
Combine like terms:
$$
(2 + 12) + (-3x - 2x) = 14 - 5x
$$
---
15) $ 32x - 4 + 23 + 2x $
Combine like terms:
$$
(32x + 2x) + (-4 + 23) = 34x + 19
$$
---
16) $ (-6)(8x - 4) + 10x $
First distribute -6:
$$
-48x + 24 + 10x = (-48x + 10x) + 24 = -38x + 24
$$
---
17) $ 14x - 5(5 - 8x) $
Distribute -5:
$$
14x - 25 + 40x = (14x + 40x) - 25 = 54x - 25
$$
---
18) $ 23x + 4(9x + 3) + 12 $
Distribute 4:
$$
23x + 36x + 12 + 12 = (23x + 36x) + (12 + 12) = 59x + 24
$$
---
19) $ 3(-7x + 5) + 20x $
Distribute 3:
$$
-21x + 15 + 20x = (-21x + 20x) + 15 = -x + 15
$$
---
20) $ 12x - 3x(x + 9) $
Distribute -3x:
$$
12x - 3x^2 - 27x = (-3x^2) + (12x - 27x) = -3x^2 - 15x
$$
---
21) $ 7x + 5x(3 - 3x) $
Distribute 5x:
$$
7x + 15x - 15x^2 = (7x + 15x) - 15x^2 = 22x - 15x^2 = -15x^2 + 22x
$$
---
22) $ 5x(-8x + 12) + 14x $
Distribute 5x:
$$
-40x^2 + 60x + 14x = -40x^2 + 74x
$$
---
23) $ 40x + 12 + 2x^2 $
Rewrite in standard form:
$$
2x^2 + 40x + 12
$$
---
24) $ 5x(x - 3) - 10 $
Distribute 5x:
$$
5x^2 - 15x - 10
$$
---
25) $ 8x - 7 + 8x + 2x^2 $
Combine like terms:
$$
2x^2 + (8x + 8x) - 7 = 2x^2 + 16x - 7
$$
---
26) $ 2x^2 - 5x - 7x $
Combine like terms:
$$
2x^2 - 12x
$$
---
27) $ 7x - 3x^2 - 5x^2 - 3 $
Combine like terms:
$$
(-3x^2 - 5x^2) + 7x - 3 = -8x^2 + 7x - 3
$$
---
28) $ 4 + x^2 - 6x^2 - 12x $
Combine like terms:
$$
(4) + (x^2 - 6x^2) - 12x = 4 - 5x^2 - 12x = -5x^2 - 12x + 4
$$
---
29) $ 12x + 8x^2 + 2x + 28 $
Combine like terms:
$$
(12x + 2x) + 8x^2 + 28 = 14x + 8x^2 + 28 = 8x^2 + 14x + 28
$$
---
30) $ 2x^2 + 6x + 3x^2 $
Combine like terms:
$$
(2x^2 + 3x^2) + 6x = 5x^2 + 6x
$$
---
31) $ 23 + 15x^2 + 8x - 4x^2 $
Combine like terms:
$$
(15x^2 - 4x^2) + 8x + 23 = 11x^2 + 8x + 23
$$
---
32) $ 8x - 12x - x^2 + 13 $
Combine like terms:
$$
(8x - 12x) - x^2 + 13 = -4x - x^2 + 13 = -x^2 - 4x + 13
$$
---
## ✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 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 + 28 $ |
| 30 | $ 5x^2 + 6x $ |
| 31 | $ 11x^2 + 8x + 23 $ |
| 32 | $ -x^2 - 4x + 13 $ |
---
Let me know if you'd like this as a printable PDF or need help understanding any specific problem!
Parent Tip: Review the logic above to help your child master the concept of simplifying algebraic expressions practice worksheet.
