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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: −12x − 18

Answer: −6(2x + 3)

  1. Highest common factor: −6
  2. −12x − 18 = −6(2x + 3)
  3. Check by expanding the brackets.
2.Factorise fully: 5x2 + 15x − 20

Answer: 5(x2+3x−4)

  1. Highest common factor: 5
  2. 5x2 + 15x − 20 = 5(x2 + 3x − 4)
  3. Check by expanding the brackets.
3.Factorise fully: 6ab − 54a

Answer: 6a(b − 9)

  1. Highest common factor: 6a
  2. 6ab − 54a = 6a(b − 9)
  3. Check by expanding the brackets.
4.Factorise fully: −15x + 3

Answer: −3(5x − 1)

  1. Highest common factor: −3
  2. −15x + 3 = −3(5x − 1)
  3. Check by expanding the brackets.
5.Factorise fully: 10x2 − 35x − 45

Answer: 5(2x2−7x−9)

  1. Highest common factor: 5
  2. 10x2 − 35x − 45 = 5(2x2 − 7x − 9)
  3. Check by expanding the brackets.
6.Factorise fully: 30ab + 35a

Answer: 5a(6b + 7)

  1. Highest common factor: 5a
  2. 30ab + 35a = 5a(6b + 7)
  3. Check by expanding the brackets.
7.Factorise fully: −9x + 27

Answer: −9(x − 3)

  1. Highest common factor: −9
  2. −9x + 27 = −9(x − 3)
  3. Check by expanding the brackets.
8.Factorise fully: 6x2 + 15x − 9

Answer: 3(2x2+5x−3)

  1. Highest common factor: 3
  2. 6x2 + 15x − 9 = 3(2x2 + 5x − 3)
  3. Check by expanding the brackets.
9.Factorise fully: 4ab − 20a

Answer: 4a(b − 5)

  1. Highest common factor: 4a
  2. 4ab − 20a = 4a(b − 5)
  3. Check by expanding the brackets.
10.Factorise fully: −4x + 32

Answer: −4(x − 8)

  1. Highest common factor: −4
  2. −4x + 32 = −4(x − 8)
  3. Check by expanding the brackets.
11.Factorise fully: 6x2 − 3x − 12

Answer: 3(2x2−x−4)

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

Answer: 5a(5b + 3)

  1. Highest common factor: 5a
  2. 25ab + 15a = 5a(5b + 3)
  3. Check by expanding the brackets.
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