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Year 8 Expanding Brackets Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

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Year 8 Expanding Brackets Worksheet — Level 3 — Practice Set 4 — Answers

Multiply every term inside the bracket. Then collect like terms.

1.Expand and simplify: (4x + 2)(x + 2)

Answer: 4x2 + 10x + 4

  1. 4x × x = 4x2
  2. 4x × 2 + 2 × x = 8x + 2x = 10x
  3. 2 × 2 = 4
2.Expand and simplify: (4x + 4)(x − 2)

Answer: 4x2 − 4x − 8

  1. 4x × x = 4x2
  2. 4x × −2 + 4 × x = −8x + 4x = −4x
  3. 4 × −2 = −8
3.Expand and simplify: (3x + 3)(x − 1)

Answer: 3x2 − 3

  1. 3x × x = 3x2
  2. 3x × −1 + 3 × x = −3x + 3x = 0
  3. 3 × −1 = −3
4.Expand and simplify: (4x + 4)(2x − 5)

Answer: 8x2 − 12x − 20

  1. 4x × 2x = 8x2
  2. 4x × −5 + 4 × 2x = −20x + 8x = −12x
  3. 4 × −5 = −20
5.Expand and simplify: (4x + 4)(x + 7)

Answer: 4x2 + 32x + 28

  1. 4x × x = 4x2
  2. 4x × 7 + 4 × x = 28x + 4x = 32x
  3. 4 × 7 = 28
6.Expand and simplify: (2x + 5)(3x + 1)

Answer: 6x2 + 17x + 5

  1. 2x × 3x = 6x2
  2. 2x × 1 + 5 × 3x = 2x + 15x = 17x
  3. 5 × 1 = 5
7.Expand and simplify: (3x − 5)(2x + 6)

Answer: 6x2 + 8x − 30

  1. 3x × 2x = 6x2
  2. 3x × 6 + −5 × 2x = 18x + −10x = 8x
  3. −5 × 6 = −30
8.Expand and simplify: (2x − 1)(2x − 1)

Answer: 4x2 − 4x + 1

  1. 2x × 2x = 4x2
  2. 2x × −1 + −1 × 2x = −2x + −2x = −4x
  3. −1 × −1 = 1
9.Expand and simplify: (4x − 3)(x + 5)

Answer: 4x2 + 17x − 15

  1. 4x × x = 4x2
  2. 4x × 5 + −3 × x = 20x + −3x = 17x
  3. −3 × 5 = −15
10.Expand and simplify: (3x − 2)(2x + 4)

Answer: 6x2 + 8x − 8

  1. 3x × 2x = 6x2
  2. 3x × 4 + −2 × 2x = 12x + −4x = 8x
  3. −2 × 4 = −8
11.Expand and simplify: (4x + 1)(3x − 1)

Answer: 12x2 − x − 1

  1. 4x × 3x = 12x2
  2. 4x × −1 + 1 × 3x = −4x + 3x = −x
  3. 1 × −1 = −1
12.Expand and simplify: (3x − 4)(3x + 6)

Answer: 9x2 + 6x − 24

  1. 3x × 3x = 9x2
  2. 3x × 6 + −4 × 3x = 18x + −12x = 6x
  3. −4 × 6 = −24
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