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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: (2x + 7)(3x + 6)

Answer: 6x2 + 33x + 42

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

Answer: 9x2 + 3x − 6

  1. 3x × 3x = 9x2
  2. 3x × 3 + −2 × 3x = 9x + −6x = 3x
  3. −2 × 3 = −6
3.Expand and simplify: (4x − 5)(3x − 1)

Answer: 12x2 − 19x + 5

  1. 4x × 3x = 12x2
  2. 4x × −1 + −5 × 3x = −4x + −15x = −19x
  3. −5 × −1 = 5
4.Expand and simplify: (2x − 6)(2x + 5)

Answer: 4x2 − 2x − 30

  1. 2x × 2x = 4x2
  2. 2x × 5 + −6 × 2x = 10x + −12x = −2x
  3. −6 × 5 = −30
5.Expand and simplify: (2x + 6)(x − 3)

Answer: 2x2 − 18

  1. 2x × x = 2x2
  2. 2x × −3 + 6 × x = −6x + 6x = 0
  3. 6 × −3 = −18
6.Expand and simplify: (3x − 1)(x + 6)

Answer: 3x2 + 17x − 6

  1. 3x × x = 3x2
  2. 3x × 6 + −1 × x = 18x + −x = 17x
  3. −1 × 6 = −6
7.Expand and simplify: (4x + 6)(2x + 6)

Answer: 8x2 + 36x + 36

  1. 4x × 2x = 8x2
  2. 4x × 6 + 6 × 2x = 24x + 12x = 36x
  3. 6 × 6 = 36
8.Expand and simplify: (3x + 6)(2x + 1)

Answer: 6x2 + 15x + 6

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

Answer: 8x2 − 28x + 12

  1. 4x × 2x = 8x2
  2. 4x × −6 + −2 × 2x = −24x + −4x = −28x
  3. −2 × −6 = 12
10.Expand and simplify: (2x + 4)(2x + 3)

Answer: 4x2 + 14x + 12

  1. 2x × 2x = 4x2
  2. 2x × 3 + 4 × 2x = 6x + 8x = 14x
  3. 4 × 3 = 12
11.Expand and simplify: (2x + 1)(3x + 6)

Answer: 6x2 + 15x + 6

  1. 2x × 3x = 6x2
  2. 2x × 6 + 1 × 3x = 12x + 3x = 15x
  3. 1 × 6 = 6
12.Expand and simplify: (2x + 7)(x − 1)

Answer: 2x2 + 5x − 7

  1. 2x × x = 2x2
  2. 2x × −1 + 7 × x = −2x + 7x = 5x
  3. 7 × −1 = −7
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