Success TutoringWorksheets

Year 8 Expanding Brackets Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic Expressions

Year 8 Expanding Brackets Worksheet — Level 3 — Answers

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

1.Expand and simplify: (2x + 5)(2x + 3)

Answer: 4x2 + 16x + 15

  1. 2x × 2x = 4x2
  2. 2x × 3 + 5 × 2x = 6x + 10x = 16x
  3. 5 × 3 = 15
2.Expand and simplify: (3x − 1)(2x − 4)

Answer: 6x2 − 14x + 4

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

Answer: 2x2 − 16x + 30

  1. 2x × x = 2x2
  2. 2x × −5 + −6 × x = −10x + −6x = −16x
  3. −6 × −5 = 30
4.Expand and simplify: (3x + 2)(2x + 2)

Answer: 6x2 + 10x + 4

  1. 3x × 2x = 6x2
  2. 3x × 2 + 2 × 2x = 6x + 4x = 10x
  3. 2 × 2 = 4
5.Expand and simplify: (4x − 1)(x + 7)

Answer: 4x2 + 27x − 7

  1. 4x × x = 4x2
  2. 4x × 7 + −1 × x = 28x + −x = 27x
  3. −1 × 7 = −7
6.Expand and simplify: (3x + 5)(x + 3)

Answer: 3x2 + 14x + 15

  1. 3x × x = 3x2
  2. 3x × 3 + 5 × x = 9x + 5x = 14x
  3. 5 × 3 = 15
7.Expand and simplify: (4x + 7)(2x + 7)

Answer: 8x2 + 42x + 49

  1. 4x × 2x = 8x2
  2. 4x × 7 + 7 × 2x = 28x + 14x = 42x
  3. 7 × 7 = 49
8.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
9.Expand and simplify: (3x + 6)(3x + 7)

Answer: 9x2 + 39x + 42

  1. 3x × 3x = 9x2
  2. 3x × 7 + 6 × 3x = 21x + 18x = 39x
  3. 6 × 7 = 42
10.Expand and simplify: (4x − 7)(2x + 2)

Answer: 8x2 − 6x − 14

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

Answer: 6x2 + 27x + 21

  1. 3x × 2x = 6x2
  2. 3x × 7 + 3 × 2x = 21x + 6x = 27x
  3. 3 × 7 = 21
12.Expand and simplify: (4x − 6)(3x − 4)

Answer: 12x2 − 34x + 24

  1. 4x × 3x = 12x2
  2. 4x × −4 + −6 × 3x = −16x + −18x = −34x
  3. −6 × −4 = 24
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: