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

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

1.Factorise fully: −5x − 40

Answer: −5(x + 8)

  1. Highest common factor: −5
  2. −5x − 40 = −5(x + 8)
  3. Check by expanding the brackets.
2.Factorise fully: 4x2 − 20x − 8

Answer: 4(x2−5x−2)

  1. Highest common factor: 4
  2. 4x2 − 20x − 8 = 4(x2 − 5x − 2)
  3. Check by expanding the brackets.
3.Factorise fully: 2ab + 4a

Answer: 2a(b + 2)

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

Answer: −2(x + 2)

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

Answer: 5(2x2−4x+1)

  1. Highest common factor: 5
  2. 10x2 − 20x + 5 = 5(2x2 − 4x + 1)
  3. Check by expanding the brackets.
6.Factorise fully: 9ab − 6a

Answer: 3a(3b − 2)

  1. Highest common factor: 3a
  2. 9ab − 6a = 3a(3b − 2)
  3. Check by expanding the brackets.
7.Factorise fully: −24x + 28

Answer: −4(6x − 7)

  1. Highest common factor: −4
  2. −24x + 28 = −4(6x − 7)
  3. Check by expanding the brackets.
8.Factorise fully: 16x2 + 12x − 4

Answer: 4(4x2+3x−1)

  1. Highest common factor: 4
  2. 16x2 + 12x − 4 = 4(4x2 + 3x − 1)
  3. Check by expanding the brackets.
9.Factorise fully: 25ab + 30a

Answer: 5a(5b + 6)

  1. Highest common factor: 5a
  2. 25ab + 30a = 5a(5b + 6)
  3. Check by expanding the brackets.
10.Factorise fully: −42x − 7

Answer: −7(6x + 1)

  1. Highest common factor: −7
  2. −42x − 7 = −7(6x + 1)
  3. Check by expanding the brackets.
11.Factorise fully: 8x2 + 4x + 12

Answer: 4(2x2+x+3)

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

Answer: 3a(6b − 5)

  1. Highest common factor: 3a
  2. 18ab − 15a = 3a(6b − 5)
  3. Check by expanding the brackets.
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