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Year 8 Expanding Brackets Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers

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

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

Answer: 6x2 − 7x − 20

  1. 2x × 3x = 6x2
  2. 2x × 4 + −5 × 3x = 8x + −15x = −7x
  3. −5 × 4 = −20
2.Expand and simplify: (2x − 5)(2x + 3)

Answer: 4x2 − 4x − 15

  1. 2x × 2x = 4x2
  2. 2x × 3 + −5 × 2x = 6x + −10x = −4x
  3. −5 × 3 = −15
3.Expand and simplify: (3x + 6)(3x + 7)

Answer: 9x2 + 39x + 42

  1. 3x × 3x = 9x2
  2. 3x × 7 + 6 × 3x = 21x + 18x = 39x
  3. 6 × 7 = 42
4.Expand and simplify: (3x + 5)(x − 3)

Answer: 3x2 − 4x − 15

  1. 3x × x = 3x2
  2. 3x × −3 + 5 × x = −9x + 5x = −4x
  3. 5 × −3 = −15
5.Expand and simplify: (3x − 5)(2x − 6)

Answer: 6x2 − 28x + 30

  1. 3x × 2x = 6x2
  2. 3x × −6 + −5 × 2x = −18x + −10x = −28x
  3. −5 × −6 = 30
6.Expand and simplify: (3x + 5)(2x + 2)

Answer: 6x2 + 16x + 10

  1. 3x × 2x = 6x2
  2. 3x × 2 + 5 × 2x = 6x + 10x = 16x
  3. 5 × 2 = 10
7.Expand and simplify: (4x + 2)(x + 3)

Answer: 4x2 + 14x + 6

  1. 4x × x = 4x2
  2. 4x × 3 + 2 × x = 12x + 2x = 14x
  3. 2 × 3 = 6
8.Expand and simplify: (4x − 3)(x − 5)

Answer: 4x2 − 23x + 15

  1. 4x × x = 4x2
  2. 4x × −5 + −3 × x = −20x + −3x = −23x
  3. −3 × −5 = 15
9.Expand and simplify: (2x − 6)(3x − 5)

Answer: 6x2 − 28x + 30

  1. 2x × 3x = 6x2
  2. 2x × −5 + −6 × 3x = −10x + −18x = −28x
  3. −6 × −5 = 30
10.Expand and simplify: (3x + 1)(x + 3)

Answer: 3x2 + 10x + 3

  1. 3x × x = 3x2
  2. 3x × 3 + 1 × x = 9x + x = 10x
  3. 1 × 3 = 3
11.Expand and simplify: (4x + 1)(x + 1)

Answer: 4x2 + 5x + 1

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

Answer: 8x2 − 18x − 35

  1. 4x × 2x = 8x2
  2. 4x × −7 + 5 × 2x = −28x + 10x = −18x
  3. 5 × −7 = −35
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