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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: (3x − 1)(x − 4)

Answer: 3x2 − 13x + 4

  1. 3x × x = 3x2
  2. 3x × −4 + −1 × x = −12x + −x = −13x
  3. −1 × −4 = 4
2.Expand and simplify: (4x + 2)(2x − 4)

Answer: 8x2 − 12x − 8

  1. 4x × 2x = 8x2
  2. 4x × −4 + 2 × 2x = −16x + 4x = −12x
  3. 2 × −4 = −8
3.Expand and simplify: (3x + 1)(x + 7)

Answer: 3x2 + 22x + 7

  1. 3x × x = 3x2
  2. 3x × 7 + 1 × x = 21x + x = 22x
  3. 1 × 7 = 7
4.Expand and simplify: (2x + 5)(3x − 2)

Answer: 6x2 + 11x − 10

  1. 2x × 3x = 6x2
  2. 2x × −2 + 5 × 3x = −4x + 15x = 11x
  3. 5 × −2 = −10
5.Expand and simplify: (4x + 5)(x − 1)

Answer: 4x2 + x − 5

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

Answer: 4x2 + 12x − 16

  1. 4x × x = 4x2
  2. 4x × 4 + −4 × x = 16x + −4x = 12x
  3. −4 × 4 = −16
7.Expand and simplify: (2x + 2)(3x − 5)

Answer: 6x2 − 4x − 10

  1. 2x × 3x = 6x2
  2. 2x × −5 + 2 × 3x = −10x + 6x = −4x
  3. 2 × −5 = −10
8.Expand and simplify: (4x − 5)(2x − 2)

Answer: 8x2 − 18x + 10

  1. 4x × 2x = 8x2
  2. 4x × −2 + −5 × 2x = −8x + −10x = −18x
  3. −5 × −2 = 10
9.Expand and simplify: (4x − 4)(3x + 3)

Answer: 12x2 − 12

  1. 4x × 3x = 12x2
  2. 4x × 3 + −4 × 3x = 12x + −12x = 0
  3. −4 × 3 = −12
10.Expand and simplify: (3x − 6)(2x − 7)

Answer: 6x2 − 33x + 42

  1. 3x × 2x = 6x2
  2. 3x × −7 + −6 × 2x = −21x + −12x = −33x
  3. −6 × −7 = 42
11.Expand and simplify: (2x + 3)(2x − 6)

Answer: 4x2 − 6x − 18

  1. 2x × 2x = 4x2
  2. 2x × −6 + 3 × 2x = −12x + 6x = −6x
  3. 3 × −6 = −18
12.Expand and simplify: (4x − 4)(2x − 6)

Answer: 8x2 − 32x + 24

  1. 4x × 2x = 8x2
  2. 4x × −6 + −4 × 2x = −24x + −8x = −32x
  3. −4 × −6 = 24
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