Let’s solve each problem step by step. We’ll expand the brackets first (multiply the number outside by each term inside), then combine like terms to simplify.
---
(a) 6(a + 2) + 3(a + 3)
→ Expand: 6×a + 6×2 + 3×a + 3×3 = 6a + 12 + 3a + 9
→ Combine: (6a + 3a) + (12 + 9) =
9a + 21
(b) 11(b - 2) + 3(b + 6)
→ Expand: 11×b - 11×2 + 3×b + 3×6 = 11b - 22 + 3b + 18
→ Combine: (11b + 3b) + (-22 + 18) =
14b - 4
(c) 3(b + 4) + 6(b - 3)
→ Expand: 3×b + 3×4 + 6×b - 6×3 = 3b + 12 + 6b - 18
→ Combine: (3b + 6b) + (12 - 18) =
9b - 6
(d) 6(c + 3) + 5(c + 12)
→ Expand: 6×c + 6×3 + 5×c + 5×12 = 6c + 18 + 5c + 60
→ Combine: (6c + 5c) + (18 + 60) =
11c + 78
(e) 8(f + 3) + 4(5 + f)
→ Expand: 8×f + 8×3 + 4×5 + 4×f = 8f + 24 + 20 + 4f
→ Combine: (8f + 4f) + (24 + 20) =
12f + 44
(f) 7(g - 2) + 3(g + 4)
→ Expand: 7×g - 7×2 + 3×g + 3×4 = 7g - 14 + 3g + 12
→ Combine: (7g + 3g) + (-14 + 12) =
10g - 2
(g) a(r + 7) + a(6 + 4r)
→ Expand: a×r + a×7 + a×6 + a×4r = ar + 7a + 6a + 4ar
→ Combine: (ar + 4ar) + (7a + 6a) =
5ar + 13a
(h) 9(k - 4) + 3(3k + 1)
→ Expand: 9×k - 9×4 + 3×3k + 3×1 = 9k - 36 + 9k + 3
→ Combine: (9k + 9k) + (-36 + 3) =
18k - 33
(i) 8(2p + 2) - 8(p + 3)
→ Expand: 8×2p + 8×2 - 8×p - 8×3 = 16p + 16 - 8p - 24
→ Combine: (16p - 8p) + (16 - 24) =
8p - 8
(j) 7(2q - 3) + 3(2q + 3)
→ Expand: 7×2q - 7×3 + 3×2q + 3×3 = 14q - 21 + 6q + 9
→ Combine: (14q + 6q) + (-21 + 9) =
20q - 12
(k) 7(10t - 2) - 2(9 + 3t)
→ Expand: 7×10t - 7×2 - 2×9 - 2×3t = 70t - 14 - 18 - 6t
→ Combine: (70t - 6t) + (-14 - 18) =
64t - 32
(l) 8(3h - 4) - 6(h + 5)
→ Expand: 8×3h - 8×4 - 6×h - 6×5 = 24h - 32 - 6h - 30
→ Combine: (24h - 6h) + (-32 - 30) =
18h - 62
(m) 7(11y + 2) - 12(y - 4)
→ Expand: 7×11y + 7×2 - 12×y + 12×4 = 77y + 14 - 12y + 48
→ Combine: (77y - 12y) + (14 + 48) =
65y + 62
(n) 2(4j - 7) + 5(4j + 7)
→ Expand: 2×4j - 2×7 + 5×4j + 5×7 = 8j - 14 + 20j + 35
→ Combine: (8j + 20j) + (-14 + 35) =
28j + 21
(o) 6(2a + 2) + 3(a + 4) + 13a
→ Expand: 6×2a + 6×2 + 3×a + 3×4 + 13a = 12a + 12 + 3a + 12 + 13a
→ Combine: (12a + 3a + 13a) + (12 + 12) =
28a + 24
(p) 3(b - 8) + 9(b + 6) - 2b
→ Expand: 3×b - 3×8 + 9×b + 9×6 - 2b = 3b - 24 + 9b + 54 - 2b
→ Combine: (3b + 9b - 2b) + (-24 + 54) =
10b + 30
---
Final Answer:
(a) 9a + 21
(b) 14b - 4
(c) 9b - 6
(d) 11c + 78
(e) 12f + 44
(f) 10g - 2
(g) 5ar + 13a
(h) 18k - 33
(i) 8p - 8
(j) 20q - 12
(k) 64t - 32
(l) 18h - 62
(m) 65y + 62
(n) 28j + 21
(o) 28a + 24
(p) 10b + 30
Parent Tip: Review the logic above to help your child master the concept of expanding fractions worksheet.
