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Year 8 Factorising Expressions (Common Factors) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers

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

1.Factorise fully: −36x − 30

Answer: −6(6x + 5)

  1. Highest common factor: −6
  2. −36x − 30 = −6(6x + 5)
  3. Check by expanding the brackets.
2.Factorise fully: 6x2 − 2x + 18

Answer: 2(3x2−x+9)

  1. Highest common factor: 2
  2. 6x2 − 2x + 18 = 2(3x2 − x + 9)
  3. Check by expanding the brackets.
3.Factorise fully: 5ab − 25a

Answer: 5a(b − 5)

  1. Highest common factor: 5a
  2. 5ab − 25a = 5a(b − 5)
  3. Check by expanding the brackets.
4.Factorise fully: −30x + 42

Answer: −6(5x − 7)

  1. Highest common factor: −6
  2. −30x + 42 = −6(5x − 7)
  3. Check by expanding the brackets.
5.Factorise fully: 12x2 − 12x − 30

Answer: 6(2x2−2x−5)

  1. Highest common factor: 6
  2. 12x2 − 12x − 30 = 6(2x2 − 2x − 5)
  3. Check by expanding the brackets.
6.Factorise fully: 15ab − 12a

Answer: 3a(5b − 4)

  1. Highest common factor: 3a
  2. 15ab − 12a = 3a(5b − 4)
  3. Check by expanding the brackets.
7.Factorise fully: −36x − 81

Answer: −9(4x + 9)

  1. Highest common factor: −9
  2. −36x − 81 = −9(4x + 9)
  3. Check by expanding the brackets.
8.Factorise fully: 20x2 − 10x − 25

Answer: 5(4x2−2x−5)

  1. Highest common factor: 5
  2. 20x2 − 10x − 25 = 5(4x2 − 2x − 5)
  3. Check by expanding the brackets.
9.Factorise fully: 10ab − 35a

Answer: 5a(2b − 7)

  1. Highest common factor: 5a
  2. 10ab − 35a = 5a(2b − 7)
  3. Check by expanding the brackets.
10.Factorise fully: −35x + 63

Answer: −7(5x − 9)

  1. Highest common factor: −7
  2. −35x + 63 = −7(5x − 9)
  3. Check by expanding the brackets.
11.Factorise fully: 6x2 − 12x + 12

Answer: 6(x2−2x+2)

  1. Highest common factor: 6
  2. 6x2 − 12x + 12 = 6(x2 − 2x + 2)
  3. Check by expanding the brackets.
12.Factorise fully: 25ab − 10a

Answer: 5a(5b − 2)

  1. Highest common factor: 5a
  2. 25ab − 10a = 5a(5b − 2)
  3. Check by expanding the brackets.
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