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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: (4x + 5)(3x + 5)

Answer: 12x2 + 35x + 25

  1. 4x × 3x = 12x2
  2. 4x × 5 + 5 × 3x = 20x + 15x = 35x
  3. 5 × 5 = 25
2.Expand and simplify: (3x − 2)(3x − 3)

Answer: 9x2 − 15x + 6

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

Answer: 2x2 − 9x + 4

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

Answer: 6x2 − 13x − 5

  1. 3x × 2x = 6x2
  2. 3x × −5 + 1 × 2x = −15x + 2x = −13x
  3. 1 × −5 = −5
5.Expand and simplify: (3x − 1)(x + 3)

Answer: 3x2 + 8x − 3

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

Answer: 8x2 − 36x + 36

  1. 4x × 2x = 8x2
  2. 4x × −6 + −6 × 2x = −24x + −12x = −36x
  3. −6 × −6 = 36
7.Expand and simplify: (2x + 3)(3x − 1)

Answer: 6x2 + 7x − 3

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

Answer: 8x2 + 16x − 10

  1. 4x × 2x = 8x2
  2. 4x × 5 + −2 × 2x = 20x + −4x = 16x
  3. −2 × 5 = −10
9.Expand and simplify: (2x − 6)(3x + 2)

Answer: 6x2 − 14x − 12

  1. 2x × 3x = 6x2
  2. 2x × 2 + −6 × 3x = 4x + −18x = −14x
  3. −6 × 2 = −12
10.Expand and simplify: (4x − 4)(x + 5)

Answer: 4x2 + 16x − 20

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

Answer: 4x2 − 10x + 4

  1. 2x × 2x = 4x2
  2. 2x × −4 + −1 × 2x = −8x + −2x = −10x
  3. −1 × −4 = 4
12.Expand and simplify: (2x − 2)(3x − 2)

Answer: 6x2 − 10x + 4

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