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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: −25x + 15

Answer: −5(5x − 3)

  1. Highest common factor: −5
  2. −25x + 15 = −5(5x − 3)
  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: 20ab + 36a

Answer: 4a(5b + 9)

  1. Highest common factor: 4a
  2. 20ab + 36a = 4a(5b + 9)
  3. Check by expanding the brackets.
4.Factorise fully: −12x − 20

Answer: −4(3x + 5)

  1. Highest common factor: −4
  2. −12x − 20 = −4(3x + 5)
  3. Check by expanding the brackets.
5.Factorise fully: 2x2 + 2x + 12

Answer: 2(x2+x+6)

  1. Highest common factor: 2
  2. 2x2 + 2x + 12 = 2(x2 + x + 6)
  3. Check by expanding the brackets.
6.Factorise fully: 9ab − 21a

Answer: 3a(3b − 7)

  1. Highest common factor: 3a
  2. 9ab − 21a = 3a(3b − 7)
  3. Check by expanding the brackets.
7.Factorise fully: −24x + 8

Answer: −8(3x − 1)

  1. Highest common factor: −8
  2. −24x + 8 = −8(3x − 1)
  3. Check by expanding the brackets.
8.Factorise fully: 8x2 + 16x − 4

Answer: 4(2x2+4x−1)

  1. Highest common factor: 4
  2. 8x2 + 16x − 4 = 4(2x2 + 4x − 1)
  3. Check by expanding the brackets.
9.Factorise fully: 8ab − 20a

Answer: 4a(2b − 5)

  1. Highest common factor: 4a
  2. 8ab − 20a = 4a(2b − 5)
  3. Check by expanding the brackets.
10.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.
11.Factorise fully: 12x2 + 24x − 54

Answer: 6(2x2+4x−9)

  1. Highest common factor: 6
  2. 12x2 + 24x − 54 = 6(2x2 + 4x − 9)
  3. Check by expanding the brackets.
12.Factorise fully: 6ab + 3a

Answer: 3a(2b + 1)

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