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

Find the highest common factor of the terms and write it outside the brackets.

1.Factorise fully: 8m + 4n

Answer: 4(2m + n)

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

Answer: 4x(x − 7)

  1. Highest common factor: 4x
  2. 4x2 − 28x = 4x(x − 7)
  3. Check by expanding the brackets.
3.Factorise fully: 15m − 35n

Answer: 5(3m − 7n)

  1. Highest common factor: 5
  2. 15m − 35n = 5(3m − 7n)
  3. Check by expanding the brackets.
4.Factorise fully: 25x2 − 40x

Answer: 5x(5x − 8)

  1. Highest common factor: 5x
  2. 25x2 − 40x = 5x(5x − 8)
  3. Check by expanding the brackets.
5.Factorise fully: 12a + 20b

Answer: 4(3a + 5b)

  1. Highest common factor: 4
  2. 12a + 20b = 4(3a + 5b)
  3. Check by expanding the brackets.
6.Factorise fully: 12x2 − 27x

Answer: 3x(4x − 9)

  1. Highest common factor: 3x
  2. 12x2 − 27x = 3x(4x − 9)
  3. Check by expanding the brackets.
7.Factorise fully: 8m + 10n

Answer: 2(4m + 5n)

  1. Highest common factor: 2
  2. 8m + 10n = 2(4m + 5n)
  3. Check by expanding the brackets.
8.Factorise fully: 6x2 − 3x

Answer: 3x(2x − 1)

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

Answer: 6(a − 2b)

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

Answer: x(x − 4)

  1. Highest common factor: x
  2. x2 − 4x = x(x − 4)
  3. Check by expanding the brackets.
11.Factorise fully: 8a − 64b

Answer: 8(a − 8b)

  1. Highest common factor: 8
  2. 8a − 64b = 8(a − 8b)
  3. Check by expanding the brackets.
12.Factorise fully: 8x2 − 28x

Answer: 4x(2x − 7)

  1. Highest common factor: 4x
  2. 8x2 − 28x = 4x(2x − 7)
  3. Check by expanding the brackets.
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