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Year 9 Factorising Expressions (Common Factors) 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 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 2 — Answers

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

1.Factorise fully: −6x − 9

Answer: −3(2x + 3)

  1. Highest common factor: −3
  2. −6x − 9 = −3(2x + 3)
  3. Check by expanding the brackets.
2.Factorise fully: 10x2 + 30x − 45

Answer: 5(2x2+6x−9)

  1. Highest common factor: 5
  2. 10x2 + 30x − 45 = 5(2x2 + 6x − 9)
  3. Check by expanding the brackets.
3.Factorise fully: 8ab − 4a

Answer: 4a(2b − 1)

  1. Highest common factor: 4a
  2. 8ab − 4a = 4a(2b − 1)
  3. Check by expanding the brackets.
4.Factorise fully: −30x + 42

Answer: −6(5x − 7)

  1. Highest common factor: −6
  2. −30x + 42 = −6(5x − 7)
  3. Check by expanding the brackets.
5.Factorise fully: 4x2 + 8x + 8

Answer: 4(x2+2x+2)

  1. Highest common factor: 4
  2. 4x2 + 8x + 8 = 4(x2 + 2x + 2)
  3. Check by expanding the brackets.
6.Factorise fully: 12ab − 14a

Answer: 2a(6b − 7)

  1. Highest common factor: 2a
  2. 12ab − 14a = 2a(6b − 7)
  3. Check by expanding the brackets.
7.Factorise fully: −9x + 3

Answer: −3(3x − 1)

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

Answer: 3(x2+2x−6)

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

Answer: 2a(6b + 1)

  1. Highest common factor: 2a
  2. 12ab + 2a = 2a(6b + 1)
  3. Check by expanding the brackets.
10.Factorise fully: −8x + 28

Answer: −4(2x − 7)

  1. Highest common factor: −4
  2. −8x + 28 = −4(2x − 7)
  3. Check by expanding the brackets.
11.Factorise fully: 6x2 + 6x − 42

Answer: 6(x2+x−7)

  1. Highest common factor: 6
  2. 6x2 + 6x − 42 = 6(x2 + x − 7)
  3. Check by expanding the brackets.
12.Factorise fully: 3ab − 6a

Answer: 3a(b − 2)

  1. Highest common factor: 3a
  2. 3ab − 6a = 3a(b − 2)
  3. Check by expanding the brackets.
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