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

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

1.Factorise fully: 35a − 42b

Answer: 7(5a − 6b)

  1. Highest common factor: 7
  2. 35a − 42b = 7(5a − 6b)
  3. Check by expanding the brackets.
2.Factorise fully: 6x2 + 16x

Answer: 2x(3x + 8)

  1. Highest common factor: 2x
  2. 6x2 + 16x = 2x(3x + 8)
  3. Check by expanding the brackets.
3.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.
4.Factorise fully: 6x2 − 14x

Answer: 2x(3x − 7)

  1. Highest common factor: 2x
  2. 6x2 − 14x = 2x(3x − 7)
  3. Check by expanding the brackets.
5.Factorise fully: 5x + 15y

Answer: 5(x + 3y)

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

Answer: 3x(x − 6)

  1. Highest common factor: 3x
  2. 3x2 − 18x = 3x(x − 6)
  3. Check by expanding the brackets.
7.Factorise fully: 36a − 30b

Answer: 6(6a − 5b)

  1. Highest common factor: 6
  2. 36a − 30b = 6(6a − 5b)
  3. Check by expanding the brackets.
8.Factorise fully: 6x2 − 48x

Answer: 6x(x − 8)

  1. Highest common factor: 6x
  2. 6x2 − 48x = 6x(x − 8)
  3. Check by expanding the brackets.
9.Factorise fully: 24m + 16n

Answer: 8(3m + 2n)

  1. Highest common factor: 8
  2. 24m + 16n = 8(3m + 2n)
  3. Check by expanding the brackets.
10.Factorise fully: 12x2 + 42x

Answer: 6x(2x + 7)

  1. Highest common factor: 6x
  2. 12x2 + 42x = 6x(2x + 7)
  3. Check by expanding the brackets.
11.Factorise fully: 5x + 10y

Answer: 5(x + 2y)

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

Answer: 3x(x − 1)

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