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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 + 4)(3x − 1)

Answer: 6x2 + 10x − 4

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

Answer: 6x2 − 2x − 28

  1. 2x × 3x = 6x2
  2. 2x × −7 + 4 × 3x = −14x + 12x = −2x
  3. 4 × −7 = −28
3.Expand and simplify: (3x − 7)(2x + 4)

Answer: 6x2 − 2x − 28

  1. 3x × 2x = 6x2
  2. 3x × 4 + −7 × 2x = 12x + −14x = −2x
  3. −7 × 4 = −28
4.Expand and simplify: (2x − 1)(2x − 5)

Answer: 4x2 − 12x + 5

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

Answer: 3x2 − 18x − 21

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

Answer: 12x2 + x − 6

  1. 4x × 3x = 12x2
  2. 4x × −2 + 3 × 3x = −8x + 9x = x
  3. 3 × −2 = −6
7.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
8.Expand and simplify: (4x + 5)(x + 5)

Answer: 4x2 + 25x + 25

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

Answer: 12x2 + 42x + 36

  1. 4x × 3x = 12x2
  2. 4x × 6 + 6 × 3x = 24x + 18x = 42x
  3. 6 × 6 = 36
10.Expand and simplify: (4x + 5)(3x − 1)

Answer: 12x2 + 11x − 5

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

Answer: 4x2 − 6x − 10

  1. 2x × 2x = 4x2
  2. 2x × −5 + 2 × 2x = −10x + 4x = −6x
  3. 2 × −5 = −10
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