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Year 8 Expanding Brackets Worksheet — Level 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 — Answers

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

1.Expand and simplify: (2x + 4)(3x + 5)

Answer: 6x2 + 22x + 20

  1. 2x × 3x = 6x2
  2. 2x × 5 + 4 × 3x = 10x + 12x = 22x
  3. 4 × 5 = 20
2.Expand and simplify: (4x + 4)(2x + 7)

Answer: 8x2 + 36x + 28

  1. 4x × 2x = 8x2
  2. 4x × 7 + 4 × 2x = 28x + 8x = 36x
  3. 4 × 7 = 28
3.Expand and simplify: (2x + 6)(3x − 5)

Answer: 6x2 + 8x − 30

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

Answer: 9x2 + 18x + 5

  1. 3x × 3x = 9x2
  2. 3x × 1 + 5 × 3x = 3x + 15x = 18x
  3. 5 × 1 = 5
5.Expand and simplify: (4x + 2)(2x + 3)

Answer: 8x2 + 16x + 6

  1. 4x × 2x = 8x2
  2. 4x × 3 + 2 × 2x = 12x + 4x = 16x
  3. 2 × 3 = 6
6.Expand and simplify: (3x + 3)(x − 2)

Answer: 3x2 − 3x − 6

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

Answer: 4x2 − 6x − 18

  1. 4x × x = 4x2
  2. 4x × −3 + 6 × x = −12x + 6x = −6x
  3. 6 × −3 = −18
9.Expand and simplify: (2x + 7)(x − 5)

Answer: 2x2 − 3x − 35

  1. 2x × x = 2x2
  2. 2x × −5 + 7 × x = −10x + 7x = −3x
  3. 7 × −5 = −35
10.Expand and simplify: (3x + 6)(2x − 3)

Answer: 6x2 + 3x − 18

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

Answer: 6x2 − 13x + 6

  1. 2x × 3x = 6x2
  2. 2x × −2 + −3 × 3x = −4x + −9x = −13x
  3. −3 × −2 = 6
12.Expand and simplify: (2x − 4)(3x − 7)

Answer: 6x2 − 26x + 28

  1. 2x × 3x = 6x2
  2. 2x × −7 + −4 × 3x = −14x + −12x = −26x
  3. −4 × −7 = 28
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