Maths Library

Expanding brackets: Year 12 maths

This topic covers multiplying out single and double brackets to form expanded algebraic expressions. The worksheet provides practise progressing from simple single brackets to expanding and simplifying pairs of binomials.

Open in full editor

What this covers

Expanding brackets is taught in Year 12 (age 16 to 17, KS5) as a topic to introduce. It sits in the Algebra strand.

Worked example

Expand and simplify: 3(2x - 4) + 2(x + 5)

  1. Expand the first bracket: 3 × 2x - 3 × 4 = 6x - 12
  2. Expand the second bracket: 2 × x + 2 × 5 = 2x + 10
  3. Collect like terms: (6x + 2x) + (-12 + 10) = 8x - 2

Answer: 8x - 2

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Single bracket with positive integer outside, e.g., 3(x + 4)
  2. Single bracket with negative multiplier or variable outside, e.g., -2(3x - 5) or x(x + 2)
  3. Expanding two single brackets and collecting like terms, e.g., 4(x + 3) - 2(x - 1)
  4. Double brackets of form (x + a)(x + b) with integers
  5. Double brackets with non-unitary x coefficients, e.g., (2x - 3)(3x + 4)

Common mistakes

  • Multiplying only the first term inside the bracket by the outside term
  • Errors with double negatives, e.g. calculating -3(x - 4) as -3x - 12

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Factorise and expand polynomials to simplify complex algebraic fractions and expressions.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Expanding brackets

Year 12 maths

Qs
6
Marks
18
NameDateScore / 18
1.
Expand and simplify (x + 4)(x + 6).
[3]
2.
Expand and simplify (x + 5)(x + 6).
[3]
3.
Expand and simplify (x + 6)(x + 6).
[3]
4.
Expand and simplify (x + 1)(x + 5).
[3]
5.
Expand and simplify (x + 8)(x + 6).
[3]
6.
Expand and simplify (x + 3)(x + 4).
[3]

Answer key

  1. x2 + 10x + 24x×x = x2, x×6 = 6x, 4×x = 4x, 4×6 = 24; Collect: x2 + 10x + 24
  2. x2 + 11x + 30x×x = x2, x×6 = 6x, 5×x = 5x, 5×6 = 30; Collect: x2 + 11x + 30
  3. x2 + 12x + 36x×x = x2, x×6 = 6x, 6×x = 6x, 6×6 = 36; Collect: x2 + 12x + 36
  4. x2 + 6x + 5x×x = x2, x×5 = 5x, 1×x = 1x, 1×5 = 5; Collect: x2 + 6x + 5
  5. x2 + 14x + 48x×x = x2, x×6 = 6x, 8×x = 8x, 8×6 = 48; Collect: x2 + 14x + 48
  6. x2 + 7x + 12x×x = x2, x×4 = 4x, 3×x = 3x, 3×4 = 12; Collect: x2 + 7x + 12