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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 3 — Answers

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

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic Expressions

Year 8 Factorising Expressions (Common Factors) Worksheet — Level 3 — Answers

Take out the highest common factor. Where the first term is negative, take out a negative factor.

1.Factorise fully: −25x − 45

Answer: −5(5x + 9)

  1. Highest common factor: −5
  2. −25x − 45 = −5(5x + 9)
  3. Check by expanding the brackets.
2.Factorise fully: 3x2 − 15x + 24

Answer: 3(x2−5x+8)

  1. Highest common factor: 3
  2. 3x2 − 15x + 24 = 3(x2 − 5x + 8)
  3. Check by expanding the brackets.
3.Factorise fully: 12ab − 30a

Answer: 6a(2b − 5)

  1. Highest common factor: 6a
  2. 12ab − 30a = 6a(2b − 5)
  3. Check by expanding the brackets.
4.Factorise fully: −6x − 3

Answer: −3(2x + 1)

  1. Highest common factor: −3
  2. −6x − 3 = −3(2x + 1)
  3. Check by expanding the brackets.
5.Factorise fully: 20x2 + 15x + 25

Answer: 5(4x2+3x+5)

  1. Highest common factor: 5
  2. 20x2 + 15x + 25 = 5(4x2 + 3x + 5)
  3. Check by expanding the brackets.
6.Factorise fully: 12ab + 28a

Answer: 4a(3b + 7)

  1. Highest common factor: 4a
  2. 12ab + 28a = 4a(3b + 7)
  3. Check by expanding the brackets.
7.Factorise fully: −15x − 12

Answer: −3(5x + 4)

  1. Highest common factor: −3
  2. −15x − 12 = −3(5x + 4)
  3. Check by expanding the brackets.
8.Factorise fully: 6x2 − 9x − 3

Answer: 3(2x2−3x−1)

  1. Highest common factor: 3
  2. 6x2 − 9x − 3 = 3(2x2 − 3x − 1)
  3. Check by expanding the brackets.
9.Factorise fully: 8ab + 6a

Answer: 2a(4b + 3)

  1. Highest common factor: 2a
  2. 8ab + 6a = 2a(4b + 3)
  3. Check by expanding the brackets.
10.Factorise fully: −18x + 3

Answer: −3(6x − 1)

  1. Highest common factor: −3
  2. −18x + 3 = −3(6x − 1)
  3. Check by expanding the brackets.
11.Factorise fully: 12x2 − 12x + 9

Answer: 3(4x2−4x+3)

  1. Highest common factor: 3
  2. 12x2 − 12x + 9 = 3(4x2 − 4x + 3)
  3. Check by expanding the brackets.
12.Factorise fully: 15ab + 35a

Answer: 5a(3b + 7)

  1. Highest common factor: 5a
  2. 15ab + 35a = 5a(3b + 7)
  3. Check by expanding the brackets.
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