Let’s solve each problem step by step. We’ll expand the brackets first (multiply the number outside by everything inside), then combine like terms to simplify.
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Section A
1)
7(y + 4) + 8
→ Expand: 7×y + 7×4 = 7y + 28
→ Add 8: 7y + 28 + 8 =
7y + 36
2)
5(b + 2) + 4
→ Expand: 5×b + 5×2 = 5b + 10
→ Add 4: 5b + 10 + 4 =
5b + 14
3)
3(a + 5) + 2a
→ Expand: 3×a + 3×5 = 3a + 15
→ Add 2a: 3a + 2a + 15 =
5a + 15
4)
2(x + 6) + 7x
→ Expand: 2×x + 2×6 = 2x + 12
→ Add 7x: 2x + 7x + 12 =
9x + 12
5)
4(9 + f) + 18f
→ Expand: 4×9 + 4×f = 36 + 4f
→ Add 18f: 4f + 18f + 36 =
22f + 36
6)
8(1 + 2g) + 5g
→ Expand: 8×1 + 8×2g = 8 + 16g
→ Add 5g: 16g + 5g + 8 =
21g + 8
7)
9 + 3(c + 4)
→ Expand: 3×c + 3×4 = 3c + 12
→ Add 9: 3c + 12 + 9 =
3c + 21
8)
11 + 5(6d + 5)
→ Expand: 5×6d + 5×5 = 30d + 25
→ Add 11: 30d + 25 + 11 =
30d + 36
9)
7x + 4(2x + 12)
→ Expand: 4×2x + 4×12 = 8x + 48
→ Add 7x: 7x + 8x + 48 =
15x + 48
10)
12a + 9(5 + 2a)
→ Expand: 9×5 + 9×2a = 45 + 18a
→ Add 12a: 12a + 18a + 45 =
30a + 45
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Section B
1)
6(3d – 1) + 8
→ Expand: 6×3d – 6×1 = 18d – 6
→ Add 8: 18d – 6 + 8 =
18d + 2
2)
5(6x – 2) + 2
→ Expand: 5×6x – 5×2 = 30x – 10
→ Add 2: 30x – 10 + 2 =
30x – 8
3)
7 – 3(8f + 6)
→ Expand: –3×8f – 3×6 = –24f – 18
→ Add 7: –24f – 18 + 7 =
–24f – 11
4)
–9 – (4j + 5)
→ This is the same as –9 –1×(4j + 5)
→ Expand: –4j – 5
→ Combine with –9: –4j – 5 – 9 =
–4j – 14
5)
8 – (1 – k)
→ Same as 8 –1×(1 – k) = 8 –1 + k
→ Simplify: 7 + k →
k + 7
6)
–2h – 4(6h – 1)
→ Expand: –4×6h + (–4)×(–1) = –24h + 4
→ Combine with –2h: –2h –24h + 4 =
–26h + 4
7)
5b(2b – 3) + 8
→ Expand: 5b×2b – 5b×3 = 10b² – 15b
→ Add 8:
10b² – 15b + 8
8)
7c(2c – 5) – 3
→ Expand: 7c×2c – 7c×5 = 14c² – 35c
→ Subtract 3:
14c² – 35c – 3
9)
9 – 2e(3 – 5e)
→ Expand: –2e×3 + (–2e)×(–5e) = –6e + 10e²
→ Rearrange: 10e² – 6e
→ Add 9:
10e² – 6e + 9
10)
xy – x(y – 1)
→ Expand: –x×y + (–x)×(–1) = –xy + x
→ Combine with xy: xy – xy + x =
x
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Final Answer:
Section A
1) 7y + 36
2) 5b + 14
3) 5a + 15
4) 9x + 12
5) 22f + 36
6) 21g + 8
7) 3c + 21
8) 30d + 36
9) 15x + 48
10) 30a + 45
Section B
1) 18d + 2
2) 30x – 8
3) –24f – 11
4) –4j – 14
5) k + 7
6) –26h + 4
7) 10b² – 15b + 8
8) 14c² – 35c – 3
9) 10e² – 6e + 9
10) x
Parent Tip: Review the logic above to help your child master the concept of expanding algebraic expressions worksheet.
