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Year 9 Expanding Brackets Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 9 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic Expressions

Year 9 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)(3x − 6)

Answer: 9x2 − 12x − 12

  1. 3x × 3x = 9x2
  2. 3x × −6 + 2 × 3x = −18x + 6x = −12x
  3. 2 × −6 = −12
2.Expand and simplify: (2x − 2)(3x − 2)

Answer: 6x2 − 10x + 4

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

Answer: 6x2 + 27x + 30

  1. 2x × 3x = 6x2
  2. 2x × 6 + 5 × 3x = 12x + 15x = 27x
  3. 5 × 6 = 30
4.Expand and simplify: (2x − 2)(2x + 4)

Answer: 4x2 + 4x − 8

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

Answer: 8x2 − 10x − 25

  1. 4x × 2x = 8x2
  2. 4x × −5 + 5 × 2x = −20x + 10x = −10x
  3. 5 × −5 = −25
6.Expand and simplify: (3x + 2)(3x − 1)

Answer: 9x2 + 3x − 2

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

Answer: 6x2 + 18x + 12

  1. 3x × 2x = 6x2
  2. 3x × 2 + 6 × 2x = 6x + 12x = 18x
  3. 6 × 2 = 12
8.Expand and simplify: (2x + 4)(2x + 7)

Answer: 4x2 + 22x + 28

  1. 2x × 2x = 4x2
  2. 2x × 7 + 4 × 2x = 14x + 8x = 22x
  3. 4 × 7 = 28
9.Expand and simplify: (4x − 5)(3x + 2)

Answer: 12x2 − 7x − 10

  1. 4x × 3x = 12x2
  2. 4x × 2 + −5 × 3x = 8x + −15x = −7x
  3. −5 × 2 = −10
10.Expand and simplify: (2x + 3)(2x + 7)

Answer: 4x2 + 20x + 21

  1. 2x × 2x = 4x2
  2. 2x × 7 + 3 × 2x = 14x + 6x = 20x
  3. 3 × 7 = 21
11.Expand and simplify: (4x − 3)(3x + 3)

Answer: 12x2 + 3x − 9

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

Answer: 6x2 − 4x − 2

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