Practice Maths

Expanding Single and Double Brackets — Solutions

Click any answer to watch the solution video.

  1. Expand single brackets

    1. 3(x + 5):
    2. 4(2y − 3):
    3. −2(a + 7):
    4. 5(3m − 4):
    5. x(x + 6):
    6. 2a(a − 3):
    7. −3p(2p + 1):
    8. 4n(n − 5):
    9. 6(2x + 3y − 1):
    10. −5k(3k − 2):

  2. Expand and simplify double brackets

    1. (x + 3)(x + 2):
    2. (y + 5)(y − 1):
    3. (a − 4)(a − 3):
    4. (2x + 1)(x + 4):
    5. (3m − 2)(m + 5):
    6. (x + 7)(x − 7):
    7. (2a + 3)(2a − 3):
    8. (4p + 1)(p − 2):
    9. (3k − 4)(2k + 3):
    10. (5x − 2)(x − 6):

  3. Special products

    1. (x + 4)2:
    2. (y − 6)2:
    3. (2a + 5)2:
    4. (3m − 1)2:
    5. (x + 9)(x − 9):
    6. (4p + 3)(4p − 3):

  4. Identify errors

    1. Jordan’s error:
    2. Priya’s error:
    3. Marcus’s error:
    4. (x + 3)(x − 3):

  5. Area, perimeter and forming expressions

    1. Rectangle area:
      1. Area:
      2. When x = 4:
    2. Square area (3a − 2)2:
    3. Width of rectangle:
    4. Consecutive even integers:
      1. Product:
      2. 8 × 10 (n = 4):

  6. Expand using special product rules

    1. (x + 4)²:
    2. (y − 6)²:
    3. (2a + 5)²:
    4. (x + 9)(x − 9):
    5. (4p + 3)(4p − 3):

  7. Spot the mistake

    1. Jordan:
    2. Priya:
    3. Marcus:
    4. Anya:

  8. Square garden and consecutive numbers

  9. Finding the width from the perimeter

  10. Multi-step expansion