GCSE Maths / Edexcel

Expanding and simplifying brackets

Expand single brackets, handle negative signs, collect like terms, and show enough working for GCSE method marks.

AlgebraFoundation and HigherGrades 3 to 6Skill

Curriculum path: GCSE Maths > Edexcel > Algebra > Expanding and simplifying brackets

Pearson Edexcel GCSE Maths algebra A4: collect like terms and multiply a single term over a bracket.

Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Expanding brackets means removing the brackets by multiplying every term inside the bracket by the term outside.

A term is a separate part of an expression, such as 2x or 3. In 4(2x + 3), both 2x and 3 must be multiplied by 4.

After expanding, simplify by collecting like terms. x terms combine with x terms, number terms combine with number terms.

If the multiplier outside the bracket is negative, it changes the sign of every term inside the bracket.

For Edexcel method marks, show the expansion before collecting like terms. Do not jump straight to an answer if signs are involved.

Key rulea(b + c) = ab + ac

Worked examples

Single bracket

Expand 4(2x + 3).

  1. Multiply the first term inside the bracket: 4 * 2x = 8x.
  2. Multiply the second term inside the bracket: 4 * 3 = 12.
  3. Put both expanded terms together.

Answer: 8x + 12

Expand and simplify

Expand and simplify 3(x + 2) + 5x.

  1. 3(x + 2) = 3x + 6
  2. 3x + 6 + 5x = 8x + 6

Answer: 8x + 6

Negative outside the bracket

Expand -2(x - 5).

  1. -2 * x = -2x
  2. -2 * -5 = +10

Answer: -2x + 10

Common mistakes

  • Multiplying only the first term inside the bracket.
  • Dropping the negative sign when the multiplier is negative.
  • Expanding correctly but forgetting to collect like terms at the end.
  • Combining x terms with number terms, such as treating 3x + 6 as 9x.

Quick exercise

Try these before moving to the exam-style questions.

  1. Expand 5(x + 2).
  2. Expand 3(2x - 4).
  3. Expand -4(x + 3).
  4. Expand and simplify 2(x + 6) + 3x.
  5. Expand and simplify 5(x - 2) - 2x.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

Expand and simplify 5(x + 2) + 3x.

expanding bracketscollecting like termsfoundation algebra
Standard exam styleFoundation and HigherNon-calculator3 marks

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

expanding bracketsnegative signssimplifying expressions
ChallengeHigherEither4 marks

A rectangle has perimeter 10x + 14. Its length is 3(x + 2). Find an expression for its width.

forming expressionsexpanding bracketsperimeterhigher reasoning