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Year 9 Expanding Brackets Worksheet — Level 3 — Practice Set 2 — Answers

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

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Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic Expressions

Year 9 Expanding Brackets Worksheet — Level 3 — Practice Set 2 — Answers

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

1.Expand and simplify: (4x + 3)(x + 4)

Answer: 4x2 + 19x + 12

  1. 4x × x = 4x2
  2. 4x × 4 + 3 × x = 16x + 3x = 19x
  3. 3 × 4 = 12
2.Expand and simplify: (3x − 2)(x − 4)

Answer: 3x2 − 14x + 8

  1. 3x × x = 3x2
  2. 3x × −4 + −2 × x = −12x + −2x = −14x
  3. −2 × −4 = 8
3.Expand and simplify: (4x + 1)(x + 5)

Answer: 4x2 + 21x + 5

  1. 4x × x = 4x2
  2. 4x × 5 + 1 × x = 20x + x = 21x
  3. 1 × 5 = 5
4.Expand and simplify: (4x + 2)(x − 4)

Answer: 4x2 − 14x − 8

  1. 4x × x = 4x2
  2. 4x × −4 + 2 × x = −16x + 2x = −14x
  3. 2 × −4 = −8
5.Expand and simplify: (2x + 1)(2x + 6)

Answer: 4x2 + 14x + 6

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

Answer: 4x2 − 12x − 16

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

Answer: 2x2 + 13x + 6

  1. 2x × x = 2x2
  2. 2x × 6 + 1 × x = 12x + x = 13x
  3. 1 × 6 = 6
8.Expand and simplify: (3x − 2)(x − 5)

Answer: 3x2 − 17x + 10

  1. 3x × x = 3x2
  2. 3x × −5 + −2 × x = −15x + −2x = −17x
  3. −2 × −5 = 10
9.Expand and simplify: (3x − 3)(2x − 1)

Answer: 6x2 − 9x + 3

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

Answer: 2x2 − 4x − 6

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

Answer: 3x2 − 16x − 35

  1. 3x × x = 3x2
  2. 3x × −7 + 5 × x = −21x + 5x = −16x
  3. 5 × −7 = −35
12.Expand and simplify: (4x − 4)(3x + 4)

Answer: 12x2 + 4x − 16

  1. 4x × 3x = 12x2
  2. 4x × 4 + −4 × 3x = 16x + −12x = 4x
  3. −4 × 4 = −16
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