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Algebraic manipulation

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1. Simplify 9x - 4 + 3x + 11.

  1. 12x - 15
  2. 6x + 7
  3. 12x + 7
  4. 12x + 15

2. Simplify 5a^2 - 3ab + 7 + 2a^2 + 8ab - 10.

  1. 7a^2 + 11ab - 3
  2. 7a^2 + 5ab - 3
  3. 7a^2 + 5ab + 17
  4. 7a^4 + 5ab - 3

3. Simplify 6xy - 2xy + 3yx + 5x^2.

  1. 12x^2y
  2. 7xy
  3. 12xy + 5x^2
  4. 7xy + 5x^2

4. Expand 4x(3x - 5y).

  1. 12x^2 - 20xy
  2. 12x^2 - 5y
  3. 7x - 20xy
  4. 12x^2 + 20xy

5. Expand -3a(2a^2 - 5a + 4).

  1. -6a^3 - 15a^2 - 12a
  2. -6a^3 + 15a^2 + 4
  3. -6a^3 + 15a^2 - 12a
  4. -6a^2 + 15a - 12

6. Expand (x + 5)(x - 2).

  1. x^2 + 7x - 10
  2. x^2 + 3x - 10
  3. x^2 - 3x - 10
  4. x^2 + 3x + 10

7. Expand (2x - 3)(x + 4).

  1. 2x^2 + 11x - 12
  2. 2x^2 - 5x - 12
  3. 2x^2 + 5x + 12
  4. 2x^2 + 5x - 12

8. Expand (2x + y)(3x - 4y).

  1. 6x^2 - 5xy - 4y^2
  2. 6x^2 - 11xy - 4y^2
  3. 6x^2 + 5xy - 4y^2
  4. 5x^2 - 5xy - 4y^2

9. Expand (x - 1)(x + 2)(x + 3).

  1. x^3 + 6x^2 + 5x - 6
  2. x^3 + 4x^2 - x - 6
  3. x^3 + 4x^2 + x - 6
  4. x^3 + 5x^2 + 6x - 6

10. Factorise fully 14x^2y - 21xy^2.

  1. 7x(2xy - 3y^2)
  2. 7xy(2x - 3y)
  3. xy(14x - 21y)
  4. 7xy(2x + 3y)

11. Factorise fully 12a^3 + 18a^2 + 6a.

  1. 6a(2a^2 + 3a + 1)
  2. 3a(4a^2 + 6a + 2)
  3. 6a(a + 1)(2a + 3)
  4. 6a(2a + 1)(a + 1)

12. Factorise px + qx + 3py + 3qy by grouping.

  1. (p + q)(x + 3y)
  2. (p + q)(3x + y)
  3. (p - q)(x + 3y)
  4. (p + 3q)(x + y)

13. Factorise fully 25x^2 - 49y^2.

  1. (5x - 7y)^2
  2. (25x - 49y)(x + y)
  3. (5x - 7y)(5x + 7y)
  4. (5x + 7y)^2

14. Factorise 9a^2 + 24ab + 16b^2.

  1. (9a + 16b)^2
  2. (3a + 4b)^2
  3. (3a - 4b)^2
  4. (9a + 4b)(a + 4b)

15. Factorise x^2 + 9x + 20.

  1. (x + 2)(x + 10)
  2. (x - 4)(x - 5)
  3. (x + 1)(x + 20)
  4. (x + 4)(x + 5)

16. Factorise x^2 - 3x - 28.

  1. (x - 7)(x + 4)
  2. (x + 7)(x - 4)
  3. (x - 14)(x + 2)
  4. (x - 7)(x - 4)

17. Factorise fully 6x^2 + 11x + 3.

  1. (6x + 1)(x + 3)
  2. (3x + 3)(2x + 1)
  3. (3x + 1)(2x + 3)
  4. (3x - 1)(2x - 3)

18. Factorise fully 8x^2 - 2x - 3.

  1. (8x + 3)(x - 1)
  2. (4x - 3)(2x + 1)
  3. (4x + 3)(2x - 1)
  4. (2x - 3)(4x + 1)

19. Factorise fully 2x^3 - 5x^2 - 3x.

  1. x(2x - 3)(x + 1)
  2. x(2x^2 - 5x - 3)
  3. x(2x - 1)(x - 3)
  4. x(2x + 1)(x - 3)

20. Factorise fully 3x^3 - 12x.

  1. 3x(x - 2)(x + 2)
  2. 3x(x^2 - 4)
  3. 3(x - 2)(x + 2)
  4. 3x(x - 4)(x + 1)

21. Write x^2 + 8x + 3 in completed-square form.

  1. (x + 8)^2 - 61
  2. (x + 4)^2 + 13
  3. (x + 4)^2 - 13
  4. (x - 4)^2 - 13

22. Write x^2 - 6x + 11 in completed-square form.

  1. (x - 6)^2 - 25
  2. (x - 3)^2 + 2
  3. (x + 3)^2 + 2
  4. (x - 3)^2 - 2

23. Write 2x^2 + 12x - 5 in completed-square form.

  1. 2(x + 6)^2 - 77
  2. (2x + 3)^2 - 14
  3. 2(x - 3)^2 - 23
  4. 2(x + 3)^2 - 23

24. Write -3x^2 + 12x + 1 in completed-square form.

  1. -3(x - 2)^2 + 13
  2. -3(x + 2)^2 + 13
  3. -3(x - 2)^2 - 11
  4. -(3x - 2)^2 + 5

Published revision 3 · 2026-09-08 · Not an official exam paper.