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

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

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic Expressions

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

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

1.Expand and simplify: (3x − 2)(x − 4)

Answer: 3x2 − 14x + 8

  1. 3x × x = 3x2
  2. 3x × −4 + −2 × x = −12x + −2x = −14x
  3. −2 × −4 = 8
2.Expand and simplify: (3x + 5)(x − 5)

Answer: 3x2 − 10x − 25

  1. 3x × x = 3x2
  2. 3x × −5 + 5 × x = −15x + 5x = −10x
  3. 5 × −5 = −25
3.Expand and simplify: (4x + 3)(3x − 5)

Answer: 12x2 − 11x − 15

  1. 4x × 3x = 12x2
  2. 4x × −5 + 3 × 3x = −20x + 9x = −11x
  3. 3 × −5 = −15
4.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
5.Expand and simplify: (4x + 2)(x + 1)

Answer: 4x2 + 6x + 2

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

Answer: 2x2 + 16x + 24

  1. 2x × x = 2x2
  2. 2x × 6 + 4 × x = 12x + 4x = 16x
  3. 4 × 6 = 24
7.Expand and simplify: (2x − 4)(x + 7)

Answer: 2x2 + 10x − 28

  1. 2x × x = 2x2
  2. 2x × 7 + −4 × x = 14x + −4x = 10x
  3. −4 × 7 = −28
8.Expand and simplify: (4x + 1)(x + 2)

Answer: 4x2 + 9x + 2

  1. 4x × x = 4x2
  2. 4x × 2 + 1 × x = 8x + x = 9x
  3. 1 × 2 = 2
9.Expand and simplify: (3x − 6)(x − 6)

Answer: 3x2 − 24x + 36

  1. 3x × x = 3x2
  2. 3x × −6 + −6 × x = −18x + −6x = −24x
  3. −6 × −6 = 36
10.Expand and simplify: (4x + 1)(x + 4)

Answer: 4x2 + 17x + 4

  1. 4x × x = 4x2
  2. 4x × 4 + 1 × x = 16x + x = 17x
  3. 1 × 4 = 4
11.Expand and simplify: (2x + 7)(x + 2)

Answer: 2x2 + 11x + 14

  1. 2x × x = 2x2
  2. 2x × 2 + 7 × x = 4x + 7x = 11x
  3. 7 × 2 = 14
12.Expand and simplify: (2x + 6)(x + 4)

Answer: 2x2 + 14x + 24

  1. 2x × x = 2x2
  2. 2x × 4 + 6 × x = 8x + 6x = 14x
  3. 6 × 4 = 24
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