Let’s go through each expression one by one and simplify them by combining like terms.
Like terms are terms that have the same variable (or no variable at all — those are just numbers). We add or subtract their coefficients (the numbers in front).
---
(a) 3a + 2b + 4a + b
→ Combine a terms: 3a + 4a = 7a
→ Combine b terms: 2b + b = 3b
✔ Final:
7a + 3b
---
(b) 7y + 5y + 2h + 2h
→ y terms: 7y + 5y = 12y
→ h terms: 2h + 2h = 4h
✔ Final:
12y + 4h
---
(c) g + 8a + 2a + g
→ g terms: g + g = 2g
→ a terms: 8a + 2a = 10a
✔ Final:
2g + 10a
---
(d) 7m + 7p + 8m + p + 2p
→ m terms: 7m + 8m = 15m
→ p terms: 7p + p + 2p = 10p
✔ Final:
15m + 10p
---
(e) 9e + 2 + e + 2
→ e terms: 9e + e = 10e
→ constants: 2 + 2 = 4
✔ Final:
10e + 4
---
(f) 4 + 3a + 2a + 8
→ a terms: 3a + 2a = 5a
→ constants: 4 + 8 = 12
✔ Final:
5a + 12
---
(g) 2y + 4 + 3y – 1
→ y terms: 2y + 3y = 5y
→ constants: 4 – 1 = 3
✔ Final:
5y + 3
---
(h) 8 + 3w – w – 3
→ w terms: 3w – w = 2w
→ constants: 8 – 3 = 5
✔ Final:
2w + 5
---
(i) 5 – 4s – 2 + 10s
→ s terms: –4s + 10s = 6s
→ constants: 5 – 2 = 3
✔ Final:
6s + 3
---
(j) 3x + 6y + 5x – 2y
→ x terms: 3x + 5x = 8x
→ y terms: 6y – 2y = 4y
✔ Final:
8x + 4y
---
(k) 6m – 2s + 11s + m
→ m terms: 6m + m = 7m
→ s terms: –2s + 11s = 9s
✔ Final:
7m + 9s
---
(l) 2a + 3b – 2 + a + 3b + 4
→ a terms: 2a + a = 3a
→ b terms: 3b + 3b = 6b
→ constants: –2 + 4 = 2
✔ Final:
3a + 6b + 2
---
(m) 3a – 2b + a – 5b
→ a terms: 3a + a = 4a
→ b terms: –2b – 5b = –7b
✔ Final:
4a – 7b
---
(n) 2x – 2y – 6x + 5y
→ x terms: 2x – 6x = –4x
→ y terms: –2y + 5y = 3y
✔ Final:
–4x + 3y
---
(o) y – 4m – 3y – 5m
→ y terms: y – 3y = –2y
→ m terms: –4m – 5m = –9m
✔ Final:
–2y – 9m
---
(p) 7p – 2q – q + 3r + 4r
→ p terms: 7p
→ q terms: –2q – q = –3q
→ r terms: 3r + 4r = 7r
✔ Final:
7p – 3q + 7r
---
(q) 11c + 8d – 6c – 11d
→ c terms: 11c – 6c = 5c
→ d terms: 8d – 11d = –3d
✔ Final:
5c – 3d
---
Final Answer:
(a) 7a + 3b
(b) 12y + 4h
(c) 2g + 10a
(d) 15m + 10p
(e) 10e + 4
(f) 5a + 12
(g) 5y + 3
(h) 2w + 5
(i) 6s + 3
(j) 8x + 4y
(k) 7m + 9s
(l) 3a + 6b + 2
(m) 4a – 7b
(n) –4x + 3y
(o) –2y – 9m
(p) 7p – 3q + 7r
(q) 5c – 3d
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions questions.
