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

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

1.Factorise fully: 21x + 28y

Answer: 7(3x + 4y)

  1. Highest common factor: 7
  2. 21x + 28y = 7(3x + 4y)
  3. Check by expanding the brackets.
2.Factorise fully: 6x2 − 12x

Answer: 6x(x − 2)

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

Answer: 3(4x + y)

  1. Highest common factor: 3
  2. 12x + 3y = 3(4x + y)
  3. Check by expanding the brackets.
4.Factorise fully: 3x2 + 12x

Answer: 3x(x + 4)

  1. Highest common factor: 3x
  2. 3x2 + 12x = 3x(x + 4)
  3. Check by expanding the brackets.
5.Factorise fully: 45x + 72y

Answer: 9(5x + 8y)

  1. Highest common factor: 9
  2. 45x + 72y = 9(5x + 8y)
  3. Check by expanding the brackets.
6.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.
7.Factorise fully: 18m − 12n

Answer: 6(3m − 2n)

  1. Highest common factor: 6
  2. 18m − 12n = 6(3m − 2n)
  3. Check by expanding the brackets.
8.Factorise fully: 20x2 − 36x

Answer: 4x(5x − 9)

  1. Highest common factor: 4x
  2. 20x2 − 36x = 4x(5x − 9)
  3. Check by expanding the brackets.
9.Factorise fully: 48m + 40n

Answer: 8(6m + 5n)

  1. Highest common factor: 8
  2. 48m + 40n = 8(6m + 5n)
  3. Check by expanding the brackets.
10.Factorise fully: 16x2 − 12x

Answer: 4x(4x − 3)

  1. Highest common factor: 4x
  2. 16x2 − 12x = 4x(4x − 3)
  3. Check by expanding the brackets.
11.Factorise fully: 27a + 72b

Answer: 9(3a + 8b)

  1. Highest common factor: 9
  2. 27a + 72b = 9(3a + 8b)
  3. Check by expanding the brackets.
12.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.
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