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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 2 — Answers

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

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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 2 — Answers

Take out the highest common factor. Where the first term is negative, take out a negative factor.

1.Factorise fully: −6x + 12

Answer: −6(x − 2)

  1. Highest common factor: −6
  2. −6x + 12 = −6(x − 2)
  3. Check by expanding the brackets.
2.Factorise fully: 16x2 − 24x + 36

Answer: 4(4x2−6x+9)

  1. Highest common factor: 4
  2. 16x2 − 24x + 36 = 4(4x2 − 6x + 9)
  3. Check by expanding the brackets.
3.Factorise fully: 36ab + 6a

Answer: 6a(6b + 1)

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

Answer: −8(6x + 1)

  1. Highest common factor: −8
  2. −48x − 8 = −8(6x + 1)
  3. Check by expanding the brackets.
5.Factorise fully: 8x2 + 8x − 28

Answer: 4(2x2+2x−7)

  1. Highest common factor: 4
  2. 8x2 + 8x − 28 = 4(2x2 + 2x − 7)
  3. Check by expanding the brackets.
6.Factorise fully: 36ab − 30a

Answer: 6a(6b − 5)

  1. Highest common factor: 6a
  2. 36ab − 30a = 6a(6b − 5)
  3. Check by expanding the brackets.
7.Factorise fully: −15x + 12

Answer: −3(5x − 4)

  1. Highest common factor: −3
  2. −15x + 12 = −3(5x − 4)
  3. Check by expanding the brackets.
8.Factorise fully: 18x2 + 24x + 12

Answer: 6(3x2+4x+2)

  1. Highest common factor: 6
  2. 18x2 + 24x + 12 = 6(3x2 + 4x + 2)
  3. Check by expanding the brackets.
9.Factorise fully: 12ab + 32a

Answer: 4a(3b + 8)

  1. Highest common factor: 4a
  2. 12ab + 32a = 4a(3b + 8)
  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: 5x2 − 25x + 30

Answer: 5(x2−5x+6)

  1. Highest common factor: 5
  2. 5x2 − 25x + 30 = 5(x2 − 5x + 6)
  3. Check by expanding the brackets.
12.Factorise fully: 9ab − 3a

Answer: 3a(3b − 1)

  1. Highest common factor: 3a
  2. 9ab − 3a = 3a(3b − 1)
  3. Check by expanding the brackets.
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