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Year 10 Factorising Expressions (Common Factors) Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 10 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Algebraic Expressions

Year 10 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: −32x + 8

Answer: −8(4x − 1)

  1. Highest common factor: −8
  2. −32x + 8 = −8(4x − 1)
  3. Check by expanding the brackets.
2.Factorise fully: 6x2 − 36x − 36

Answer: 6(x2−6x−6)

  1. Highest common factor: 6
  2. 6x2 − 36x − 36 = 6(x2 − 6x − 6)
  3. Check by expanding the brackets.
3.Factorise fully: 4ab + 16a

Answer: 4a(b + 4)

  1. Highest common factor: 4a
  2. 4ab + 16a = 4a(b + 4)
  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: 4x2 + 12x + 36

Answer: 4(x2+3x+9)

  1. Highest common factor: 4
  2. 4x2 + 12x + 36 = 4(x2 + 3x + 9)
  3. Check by expanding the brackets.
6.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.
7.Factorise fully: −6x + 4

Answer: −2(3x − 2)

  1. Highest common factor: −2
  2. −6x + 4 = −2(3x − 2)
  3. Check by expanding the brackets.
8.Factorise fully: 12x2 + 16x + 24

Answer: 4(3x2+4x+6)

  1. Highest common factor: 4
  2. 12x2 + 16x + 24 = 4(3x2 + 4x + 6)
  3. Check by expanding the brackets.
9.Factorise fully: 15ab − 18a

Answer: 3a(5b − 6)

  1. Highest common factor: 3a
  2. 15ab − 18a = 3a(5b − 6)
  3. Check by expanding the brackets.
10.Factorise fully: −16x − 8

Answer: −8(2x + 1)

  1. Highest common factor: −8
  2. −16x − 8 = −8(2x + 1)
  3. Check by expanding the brackets.
11.Factorise fully: 18x2 + 42x − 6

Answer: 6(3x2+7x−1)

  1. Highest common factor: 6
  2. 18x2 + 42x − 6 = 6(3x2 + 7x − 1)
  3. Check by expanding the brackets.
12.Factorise fully: 4ab − 12a

Answer: 4a(b − 3)

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