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Year 9 Expanding Brackets Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 9 algebraic expressions worksheet.

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Year 9 Expanding Brackets Worksheet — Level 3 — Practice Set 4 — Answers

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

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

Answer: 9x2 − 9

  1. 3x × 3x = 9x2
  2. 3x × −3 + 3 × 3x = −9x + 9x = 0
  3. 3 × −3 = −9
2.Expand and simplify: (3x − 5)(2x + 5)

Answer: 6x2 + 5x − 25

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

Answer: 6x2 + 32x + 42

  1. 3x × 2x = 6x2
  2. 3x × 6 + 7 × 2x = 18x + 14x = 32x
  3. 7 × 6 = 42
4.Expand and simplify: (4x + 5)(3x − 4)

Answer: 12x2 − x − 20

  1. 4x × 3x = 12x2
  2. 4x × −4 + 5 × 3x = −16x + 15x = −x
  3. 5 × −4 = −20
5.Expand and simplify: (3x + 3)(2x − 1)

Answer: 6x2 + 3x − 3

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

Answer: 9x2 − 15x + 6

  1. 3x × 3x = 9x2
  2. 3x × −2 + −3 × 3x = −6x + −9x = −15x
  3. −3 × −2 = 6
7.Expand and simplify: (3x − 4)(x + 7)

Answer: 3x2 + 17x − 28

  1. 3x × x = 3x2
  2. 3x × 7 + −4 × x = 21x + −4x = 17x
  3. −4 × 7 = −28
8.Expand and simplify: (3x − 1)(x − 2)

Answer: 3x2 − 7x + 2

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

Answer: 9x2 − 12x + 3

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

Answer: 6x2 − x − 35

  1. 2x × 3x = 6x2
  2. 2x × 7 + −5 × 3x = 14x + −15x = −x
  3. −5 × 7 = −35
11.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
12.Expand and simplify: (4x + 4)(x − 3)

Answer: 4x2 − 8x − 12

  1. 4x × x = 4x2
  2. 4x × −3 + 4 × x = −12x + 4x = −8x
  3. 4 × −3 = −12
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