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Factorise sums and differences of cubes

11th grade (Year 12 in England) · 16 questions · Common Core: HSA.SSE.A.2, HSA.APR.C.4

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  1. Question 1

    Factorise: 8x³ − 27

    • A. (2x − 3)³
    • B. (2x − 3)(4x² + 6x + 9)
    • C. (8x − 27)(x² + 1)
    • D. (2x − 3)(4x² − 6x + 9)

  2. Question 2

    Factorise: x³ − 125

    • A. (x − 5)(x² + 5x + 25)
    • B. (x − 5)³
    • C. (x + 5)(x² − 5x + 25)
    • D. (x − 5)(x² − 5x + 25)

  3. Question 3

    Factorise: 8x³ − 1

    • A. (2x − 1)(4x² + 2x + 1)
    • B. (2x − 1)(2x² + 1x + 1)
    • C. (2x − 1)(4x² − 2x + 1)
    • D. (2x − 1)³

  4. Question 4

    Factorise: x³ + 216

    • A. (x + 6)(x² − 6x + 36)
    • B. (x + 6)(x² + 6x + 36)
    • C. (x + 6)(x² − 12x + 36)
    • D. (x + 6)³

  5. Question 5

    Factorise: 64x³ + 1

    • A. (4x + 1)³
    • B. (4x + 1)(16x² − 4x + 1)
    • C. (4x + 1)(16x² + 4x + 1)
    • D. (4x + 1)(4x² − 1x + 1)

  6. Question 6

    Factorise: x³ + 64

    • A. (x + 4)(x² − 8x + 16)
    • B. (x + 4)³
    • C. (x + 4)(x² + 4x + 16)
    • D. (x + 4)(x² − 4x + 16)

  7. Question 7

    Factorise: 8x³ − 27

    • A. (2x − 3)(4x² + 6x + 9)
    • B. (8x − 27)(x² + 1)
    • C. (2x − 3)(4x² − 6x + 9)
    • D. (2x − 3)³

  8. Question 8

    Factorise: x³ + 27

    • A. (x + 3)³
    • B. (x + 3)(x² − 3x + 9)
    • C. (x + 3)(x² + 3x + 9)
    • D. (x + 3)(x² − 6x + 9)

  9. Question 9

    Factorise: 27x³ + 64

    • A. (3x + 4)(9x² − 12x + 16)
    • B. (3x + 4)(9x² + 12x + 16)
    • C. (3x + 4)³
    • D. (3x + 4)(3x² − 4x + 4)

  10. Question 10

    Factorise: x³ − 8

    • A. (x − 2)(x² + 2x + 4)
    • B. (x − 2)(x² − 2x + 4)
    • C. (x − 2)³
    • D. (x + 2)(x² − 2x + 4)

  11. Question 11

    Factorise: 8x³ − 27

    • A. (8x − 27)(x² + 1)
    • B. (2x − 3)(4x² + 6x + 9)
    • C. (2x − 3)³
    • D. (2x − 3)(4x² − 6x + 9)

  12. Question 12

    Factorise: x³ + 1

    • A. (x + 1)(x² − 2x + 1)
    • B. (x + 1)³
    • C. (x + 1)(x² − 1x + 1)
    • D. (x + 1)(x² + 1x + 1)

  13. Question 13

    Factorise: 8x³ − 27

    • A. (8x − 27)(x² + 1)
    • B. (2x − 3)(4x² + 6x + 9)
    • C. (2x − 3)³
    • D. (2x − 3)(4x² − 6x + 9)

  14. Question 14

    Factorise: x³ − 27

    • A. (x + 3)(x² − 3x + 9)
    • B. (x − 3)(x² + 3x + 9)
    • C. (x − 3)(x² − 3x + 9)
    • D. (x − 3)³

  15. Question 15

    Factorise: 8x³ − 27

    • A. (2x − 3)(4x² − 6x + 9)
    • B. (2x − 3)(4x² + 6x + 9)
    • C. (2x − 3)(2x² + 3x + 3)
    • D. (2x − 3)³

  16. Question 16

    Factorise: x³ + 27

    • A. (x + 3)(x² + 3x + 9)
    • B. (x + 3)(x² − 6x + 9)
    • C. (x + 3)(x² − 3x + 9)
    • D. (x + 3)³

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Answer key: Factorise sums and differences of cubes

  1. 1. B. (2x − 3)(4x² + 6x + 9)

  2. 2. A. (x − 5)(x² + 5x + 25)

  3. 3. A. (2x − 1)(4x² + 2x + 1)

  4. 4. A. (x + 6)(x² − 6x + 36)

  5. 5. B. (4x + 1)(16x² − 4x + 1)

  6. 6. D. (x + 4)(x² − 4x + 16)

  7. 7. A. (2x − 3)(4x² + 6x + 9)

  8. 8. B. (x + 3)(x² − 3x + 9)

  9. 9. A. (3x + 4)(9x² − 12x + 16)

  10. 10. A. (x − 2)(x² + 2x + 4)

  11. 11. B. (2x − 3)(4x² + 6x + 9)

  12. 12. C. (x + 1)(x² − 1x + 1)

  13. 13. B. (2x − 3)(4x² + 6x + 9)

  14. 14. B. (x − 3)(x² + 3x + 9)

  15. 15. B. (2x − 3)(4x² + 6x + 9)

  16. 16. C. (x + 3)(x² − 3x + 9)