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

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

1.Factorise fully: −16x − 28

Answer: −4(4x + 7)

  1. Highest common factor: −4
  2. −16x − 28 = −4(4x + 7)
  3. Check by expanding the brackets.
2.Factorise fully: 15x2 + 5x − 15

Answer: 5(3x2+x−3)

  1. Highest common factor: 5
  2. 15x2 + 5x − 15 = 5(3x2 + x − 3)
  3. Check by expanding the brackets.
3.Factorise fully: 12ab + 54a

Answer: 6a(2b + 9)

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

Answer: −4(x + 1)

  1. Highest common factor: −4
  2. −4x − 4 = −4(x + 1)
  3. Check by expanding the brackets.
5.Factorise fully: 6x2 + 24x + 30

Answer: 6(x2+4x+5)

  1. Highest common factor: 6
  2. 6x2 + 24x + 30 = 6(x2 + 4x + 5)
  3. Check by expanding the brackets.
6.Factorise fully: 24ab + 6a

Answer: 6a(4b + 1)

  1. Highest common factor: 6a
  2. 24ab + 6a = 6a(4b + 1)
  3. Check by expanding the brackets.
7.Factorise fully: −30x − 25

Answer: −5(6x + 5)

  1. Highest common factor: −5
  2. −30x − 25 = −5(6x + 5)
  3. Check by expanding the brackets.
8.Factorise fully: 5x2 + 15x + 15

Answer: 5(x2+3x+3)

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

Answer: 4a(5b + 3)

  1. Highest common factor: 4a
  2. 20ab + 12a = 4a(5b + 3)
  3. Check by expanding the brackets.
10.Factorise fully: −18x − 63

Answer: −9(2x + 7)

  1. Highest common factor: −9
  2. −18x − 63 = −9(2x + 7)
  3. Check by expanding the brackets.
11.Factorise fully: 6x2 + 4x − 8

Answer: 2(3x2+2x−4)

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

Answer: 3a(5b − 4)

  1. Highest common factor: 3a
  2. 15ab − 12a = 3a(5b − 4)
  3. Check by expanding the brackets.
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