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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 8 algebraic expressions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 8 · Mathematics · Algebraic Expressions

Year 8 Factorising Expressions (Common Factors) Worksheet — Level 2 — Practice Set 4 — Answers

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

1.Factorise fully: 12m − 15n

Answer: 3(4m − 5n)

  1. Highest common factor: 3
  2. 12m − 15n = 3(4m − 5n)
  3. Check by expanding the brackets.
2.Factorise fully: 3x2 + 15x

Answer: 3x(x + 5)

  1. Highest common factor: 3x
  2. 3x2 + 15x = 3x(x + 5)
  3. Check by expanding the brackets.
3.Factorise fully: 18a − 30b

Answer: 6(3a − 5b)

  1. Highest common factor: 6
  2. 18a − 30b = 6(3a − 5b)
  3. Check by expanding the brackets.
4.Factorise fully: 20x2 + 4x

Answer: 4x(5x + 1)

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

Answer: 9(x − y)

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

Answer: 3x(5x − 1)

  1. Highest common factor: 3x
  2. 15x2 − 3x = 3x(5x − 1)
  3. Check by expanding the brackets.
7.Factorise fully: 8m − 18n

Answer: 2(4m − 9n)

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

Answer: 2x(x + 4)

  1. Highest common factor: 2x
  2. 2x2 + 8x = 2x(x + 4)
  3. Check by expanding the brackets.
9.Factorise fully: 24a + 28b

Answer: 4(6a + 7b)

  1. Highest common factor: 4
  2. 24a + 28b = 4(6a + 7b)
  3. Check by expanding the brackets.
10.Factorise fully: 3x2 + 5x

Answer: x(3x + 5)

  1. Highest common factor: x
  2. 3x2 + 5x = x(3x + 5)
  3. Check by expanding the brackets.
11.Factorise fully: 42a + 35b

Answer: 7(6a + 5b)

  1. Highest common factor: 7
  2. 42a + 35b = 7(6a + 5b)
  3. Check by expanding the brackets.
12.Factorise fully: 6x2 + 42x

Answer: 6x(x + 7)

  1. Highest common factor: 6x
  2. 6x2 + 42x = 6x(x + 7)
  3. Check by expanding the brackets.
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