To simplify algebraic expressions, we
combine like terms. Like terms are terms that have the same variable raised to the same power (or are constants). We add or subtract their coefficients.
Let’s go through each expression one by one:
---
1. `a + a + a + a`
→ 4 terms of `a` → `4a`
✔ Simplified: `4a`
---
2. `s + s + s - s`
→ 3s - s = 2s
✔ Simplified: `2s`
---
3. `p + p + p - p - p`
→ 3p - 2p = p
✔ Simplified: `p`
---
4. `c + c + c + c + d + d`
→ 4c + 2d
✔ Simplified: `4c + 2d`
---
5. `g + g + u + u`
→ 2g + 2u
✔ Simplified: `2g + 2u`
---
6. `a + b + a + b + a`
→ a + a + a = 3a; b + b = 2b → `3a + 2b`
✔ Simplified: `3a + 2b`
---
7. `k + c + f + f + c + k`
→ k + k = 2k; c + c = 2c; f + f = 2f → `2k + 2c + 2f`
✔ Simplified: `2k + 2c + 2f`
---
8. `m + m + a + a - m`
→ m + m - m = m; a + a = 2a → `m + 2a`
✔ Simplified: `m + 2a`
---
9. `f + 3r + 6f - 3r`
→ f + 6f = 7f; 3r - 3r = 0 → `7f`
✔ Simplified: `7f`
---
10. `12g + m - 7g + 4m - g`
→ g terms: 12g - 7g - g = 4g
→ m terms: m + 4m = 5m
→ `4g + 5m`
✔ Simplified: `4g + 5m`
---
11. `4s + s + 2s`
→ 4s + s + 2s = 7s
✔ Simplified: `7s`
---
12. `7x - 2x + 3x`
→ 7x - 2x = 5x; 5x + 3x = 8x
✔ Simplified: `8x`
---
13. `10d + 7b - 2b - 4d`
→ d terms: 10d - 4d = 6d
→ b terms: 7b - 2b = 5b
→ `6d + 5b`
✔ Simplified: `6d + 5b`
---
14. `8n + 6k + 4z - 6n + z - 5k`
→ n terms: 8n - 6n = 2n
→ k terms: 6k - 5k = k
→ z terms: 4z + z = 5z
→ `2n + k + 5z`
✔ Simplified: `2n + k + 5z`
---
15. `p + 14v + 10p - 5v + 7 - 2p + 3`
→ p terms: p + 10p - 2p = 9p
→ v terms: 14v - 5v = 9v
→ constants: 7 + 3 = 10
→ `9p + 9v + 10`
✔ Simplified: `9p + 9v + 10`
---
16. `f + 3r + 6f - r + 5`
→ f terms: f + 6f = 7f
→ r terms: 3r - r = 2r
→ constant: 5
→ `7f + 2r + 5`
✔ Simplified: `7f + 2r + 5`
---
17. `12h + 30 - 4h - 25 + 16m`
→ h terms: 12h - 4h = 8h
→ constants: 30 - 25 = 5
→ m term: 16m
→ `8h + 16m + 5`
✔ Simplified: `8h + 16m + 5`
---
18. `20f + 11m - 9f + 10 - 3`
→ f terms: 20f - 9f = 11f
→ m term: 11m
→ constants: 10 - 3 = 7
→ `11f + 11m + 7`
✔ Simplified: `11f + 11m + 7`
---
✔ Final Answer Table:
| No. | Simplified Algebraic Expression |
|-----|----------------------------------|
| 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 |
---
Summary: Always group and combine like terms — variables with the same letter and exponent, and constants. This reduces the expression to its simplest form.
Parent Tip: Review the logic above to help your child master the concept of simplify equations worksheet.
