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Year 10 Expanding Brackets Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 10 algebraic expressions worksheet.

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Year 10 Expanding Brackets Worksheet — Level 3 — Practice Set 4 — Answers

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

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

Answer: 3x2 − 8x + 5

  1. 3x × x = 3x2
  2. 3x × −1 + −5 × x = −3x + −5x = −8x
  3. −5 × −1 = 5
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: (2x − 3)(x − 2)

Answer: 2x2 − 7x + 6

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

Answer: 8x2 − 10x − 42

  1. 4x × 2x = 8x2
  2. 4x × −6 + 7 × 2x = −24x + 14x = −10x
  3. 7 × −6 = −42
5.Expand and simplify: (4x − 3)(3x + 4)

Answer: 12x2 + 7x − 12

  1. 4x × 3x = 12x2
  2. 4x × 4 + −3 × 3x = 16x + −9x = 7x
  3. −3 × 4 = −12
6.Expand and simplify: (2x + 5)(3x − 5)

Answer: 6x2 + 5x − 25

  1. 2x × 3x = 6x2
  2. 2x × −5 + 5 × 3x = −10x + 15x = 5x
  3. 5 × −5 = −25
7.Expand and simplify: (4x + 7)(x + 6)

Answer: 4x2 + 31x + 42

  1. 4x × x = 4x2
  2. 4x × 6 + 7 × x = 24x + 7x = 31x
  3. 7 × 6 = 42
8.Expand and simplify: (3x + 6)(2x + 6)

Answer: 6x2 + 30x + 36

  1. 3x × 2x = 6x2
  2. 3x × 6 + 6 × 2x = 18x + 12x = 30x
  3. 6 × 6 = 36
9.Expand and simplify: (4x + 7)(x − 4)

Answer: 4x2 − 9x − 28

  1. 4x × x = 4x2
  2. 4x × −4 + 7 × x = −16x + 7x = −9x
  3. 7 × −4 = −28
10.Expand and simplify: (2x − 3)(2x − 2)

Answer: 4x2 − 10x + 6

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

Answer: 12x2 − 2x − 2

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

Answer: 6x2 − 3x − 30

  1. 2x × 3x = 6x2
  2. 2x × 6 + −5 × 3x = 12x + −15x = −3x
  3. −5 × 6 = −30
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