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Year 10 Expanding Brackets Worksheet — Level 3 — Answers

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

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Year 10 · Mathematics · Algebraic Expressions

Year 10 Expanding Brackets Worksheet — Level 3 — Answers

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

1.Expand and simplify: (4x + 7)(2x − 5)

Answer: 8x2 − 6x − 35

  1. 4x × 2x = 8x2
  2. 4x × −5 + 7 × 2x = −20x + 14x = −6x
  3. 7 × −5 = −35
2.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
3.Expand and simplify: (2x − 2)(x − 1)

Answer: 2x2 − 4x + 2

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

Answer: 4x2 − 4x − 24

  1. 2x × 2x = 4x2
  2. 2x × −6 + 4 × 2x = −12x + 8x = −4x
  3. 4 × −6 = −24
5.Expand and simplify: (2x + 7)(x + 2)

Answer: 2x2 + 11x + 14

  1. 2x × x = 2x2
  2. 2x × 2 + 7 × x = 4x + 7x = 11x
  3. 7 × 2 = 14
6.Expand and simplify: (4x + 3)(2x − 1)

Answer: 8x2 + 2x − 3

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

Answer: 4x2 − 12x − 7

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

Answer: 6x2 − x − 12

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

Answer: 9x2 − 6x + 1

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

Answer: 8x2 + 6x − 9

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

Answer: 4x2 + 20x + 21

  1. 2x × 2x = 4x2
  2. 2x × 3 + 7 × 2x = 6x + 14x = 20x
  3. 7 × 3 = 21
12.Expand and simplify: (4x − 6)(x + 1)

Answer: 4x2 − 2x − 6

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