Simplify algebraic expressions worksheet with 18 problems for practice.

Explanation:
We need to simplify each algebraic expression by combining like terms. Like terms are terms that have the same variable(s) raised to the same power (e.g., all “a” terms, all “s” terms, constants, etc.). We add or subtract their coefficients.

Let’s go one by one:

1. a + a + a + a
Four a’s → 4a

2. s + s + s − s
s + s + s = 3s; 3s − s = 2s

3. p + p + p − p − p
p + p + p = 3p; 3p − p − p = 3p − 2p = p

4. c + c + c + c + d + d
Four c’s → 4c; two d’s → 2d → 4c + 2d

5. g + g + u + u
Two g’s → 2g; two u’s → 2u → 2g + 2u

6. a + b + a + b + a
a + a + a = 3a; b + b = 2b → 3a + 2b

7. k + c + f + f + c + k
k + k = 2k; c + c = 2c; f + f = 2f → 2k + 2c + 2f

8. m + m + a + a − m
m + m − m = m; a + a = 2a → m + 2a

9. f + 3r + 6f − 3r
f + 6f = 7f; 3r − 3r = 0 → 7f

10. 12g + m − 7g + 4m − g
g terms: 12g − 7g − g = 4g
m terms: m + 4m = 5m
→ 4g + 5m

11. 4s + s + 2s
4s + s + 2s = 7s

12. 7x − 2x + 3x
7x − 2x = 5x; 5x + 3x = 8x

13. 10d + 7b − 2b − 4d
d: 10d − 4d = 6d
b: 7b − 2b = 5b
→ 6d + 5b

14. 8n + 6k + 4z − 6n + z − 5k
n: 8n − 6n = 2n
k: 6k − 5k = k
z: 4z + z = 5z
→ 2n + k + 5z

15. p + 14v + 10p − 5v + 7 − 2p + 3
p: p + 10p − 2p = 9p
v: 14v − 5v = 9v
constants: 7 + 3 = 10
→ 9p + 9v + 10

16. f + 3r + 6f − r + 5
f: f + 6f = 7f
r: 3r − r = 2r
constant: +5
→ 7f + 2r + 5

17. 12h + 30 − 4h − 25 + 16m
h: 12h − 4h = 8h
constants: 30 − 25 = 5
m: 16m
→ 8h + 16m + 5

18. 20f + 11m − 9f + 10 − 3
f: 20f − 9f = 11f
m: 11m
constants: 10 − 3 = 7
→ 11f + 11m + 7

Let me double-check a few tricky ones:

- #3: p + p + p − p − p = (3p) − (2p) = p ✔
- #10: 12g − 7g − g = 4g; m + 4m = 5m → 4g + 5m ✔
- #15: p terms: 1+10−2=9; v: 14−5=9; const: 7+3=10 → 9p+9v+10 ✔
- #18: 20f−9f=11f; 11m stays; 10−3=7 → 11f+11m+7 ✔

All look correct.

Final Answer:
1. 4a
2. 2s
3. p
4. 4c + 2d
5. 2g + 2u
6. 3a + 2b
7. 2k + 2c + 2f
8. m + 2a
9. 7f
10. 4g + 5m
11. 7s
12. 8x
13. 6d + 5b
14. 2n + k + 5z
15. 9p + 9v + 10
16. 7f + 2r + 5
17. 8h + 16m + 5
18. 11f + 11m + 7