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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: −30x + 48

Answer: −6(5x − 8)

  1. Highest common factor: −6
  2. −30x + 48 = −6(5x − 8)
  3. Check by expanding the brackets.
2.Factorise fully: 10x2 + 5x − 45

Answer: 5(2x2+x−9)

  1. Highest common factor: 5
  2. 10x2 + 5x − 45 = 5(2x2 + x − 9)
  3. Check by expanding the brackets.
3.Factorise fully: 15ab + 25a

Answer: 5a(3b + 5)

  1. Highest common factor: 5a
  2. 15ab + 25a = 5a(3b + 5)
  3. Check by expanding the brackets.
4.Factorise fully: −25x + 30

Answer: −5(5x − 6)

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

Answer: 2(3x2+x−6)

  1. Highest common factor: 2
  2. 6x2 + 2x − 12 = 2(3x2 + x − 6)
  3. Check by expanding the brackets.
6.Factorise fully: 25ab + 20a

Answer: 5a(5b + 4)

  1. Highest common factor: 5a
  2. 25ab + 20a = 5a(5b + 4)
  3. Check by expanding the brackets.
7.Factorise fully: −10x − 16

Answer: −2(5x + 8)

  1. Highest common factor: −2
  2. −10x − 16 = −2(5x + 8)
  3. Check by expanding the brackets.
8.Factorise fully: 3x2 + 18x − 18

Answer: 3(x2+6x−6)

  1. Highest common factor: 3
  2. 3x2 + 18x − 18 = 3(x2 + 6x − 6)
  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: −12x − 21

Answer: −3(4x + 7)

  1. Highest common factor: −3
  2. −12x − 21 = −3(4x + 7)
  3. Check by expanding the brackets.
11.Factorise fully: 9x2 − 6x − 6

Answer: 3(3x2−2x−2)

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

Answer: 4a(b − 3)

  1. Highest common factor: 4a
  2. 4ab − 12a = 4a(b − 3)
  3. Check by expanding the brackets.
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