Success TutoringWorksheets

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

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

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 9 · Mathematics · Algebraic Expressions

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

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

1.Expand and simplify: (4x − 3)(2x − 1)

Answer: 8x2 − 10x + 3

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

Answer: 12x2 − 5x − 2

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

Answer: 3x2 + 17x − 6

  1. 3x × x = 3x2
  2. 3x × 6 + −1 × x = 18x + −x = 17x
  3. −1 × 6 = −6
4.Expand and simplify: (3x − 2)(2x − 5)

Answer: 6x2 − 19x + 10

  1. 3x × 2x = 6x2
  2. 3x × −5 + −2 × 2x = −15x + −4x = −19x
  3. −2 × −5 = 10
5.Expand and simplify: (4x + 2)(2x + 5)

Answer: 8x2 + 24x + 10

  1. 4x × 2x = 8x2
  2. 4x × 5 + 2 × 2x = 20x + 4x = 24x
  3. 2 × 5 = 10
6.Expand and simplify: (3x − 1)(3x + 1)

Answer: 9x2 − 1

  1. 3x × 3x = 9x2
  2. 3x × 1 + −1 × 3x = 3x + −3x = 0
  3. −1 × 1 = −1
7.Expand and simplify: (4x + 7)(2x + 2)

Answer: 8x2 + 22x + 14

  1. 4x × 2x = 8x2
  2. 4x × 2 + 7 × 2x = 8x + 14x = 22x
  3. 7 × 2 = 14
8.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
9.Expand and simplify: (4x + 4)(3x + 2)

Answer: 12x2 + 20x + 8

  1. 4x × 3x = 12x2
  2. 4x × 2 + 4 × 3x = 8x + 12x = 20x
  3. 4 × 2 = 8
10.Expand and simplify: (3x + 2)(2x − 1)

Answer: 6x2 + x − 2

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

Answer: 12x2 − 23x + 10

  1. 4x × 3x = 12x2
  2. 4x × −2 + −5 × 3x = −8x + −15x = −23x
  3. −5 × −2 = 10
12.Expand and simplify: (2x − 2)(3x − 3)

Answer: 6x2 − 12x + 6

  1. 2x × 3x = 6x2
  2. 2x × −3 + −2 × 3x = −6x + −6x = −12x
  3. −2 × −3 = 6
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: