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AQASpec A1-A4Foundation & Higher~30 min

Algebraic Expressions

Mathematics · Topic revision workspace

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Topic overview

What you need to know

Algebraic Expressions is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A letter or symbol used to represent an unknown value in an expression or equation, e.g. x, y. A single number, variable, or number multiplied by a variable, e.g. 3x, −5, 2y². The number in front of a variable. In 5x, the coefficient is 5.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

  • Variable: A letter or symbol used to represent an unknown value in an expression or equation, e.g. x, y.
  • Term: A single number, variable, or number multiplied by a variable, e.g. 3x, −5, 2y².
  • Coefficient: The number in front of a variable. In 5x, the coefficient is 5.
  • Collecting Like Terms: Simplifying an expression by combining terms with the same variable and power. E.g. 3x + 5x = 8x.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

  • Expanding Single Brackets: Multiply each term inside the bracket by the term outside. E.g. 3(x + 4) = 3x + 12.
  • Expanding Double Brackets: Use FOIL: multiply First, Outer, Inner, Last terms. E.g. (x+3)(x+2) = x² + 5x + 6.
  • Factorising (Single Bracket): Take out the highest common factor. E.g. 6x + 9 = 3(2x + 3).
  • Factorising Quadratics: Write ax² + bx + c as a product of two brackets. E.g. x² + 5x + 6 = (x+2)(x+3).

Core knowledge

Key facts for Algebraic Expressions

1

Variable

A letter or symbol used to represent an unknown value in an expression or equation, e.g. x, y.

2

Term

A single number, variable, or number multiplied by a variable, e.g. 3x, −5, 2y².

3

Coefficient

The number in front of a variable. In 5x, the coefficient is 5.

4

Collecting Like Terms

Simplifying an expression by combining terms with the same variable and power. E.g. 3x + 5x = 8x.

5

Expanding Single Brackets

Multiply each term inside the bracket by the term outside. E.g. 3(x + 4) = 3x + 12.

6

Expanding Double Brackets

Use FOIL: multiply First, Outer, Inner, Last terms. E.g. (x+3)(x+2) = x² + 5x + 6.

7

Factorising (Single Bracket)

Take out the highest common factor. E.g. 6x + 9 = 3(2x + 3).

8

Factorising Quadratics

Write ax² + bx + c as a product of two brackets. E.g. x² + 5x + 6 = (x+2)(x+3).

Active recall

Close the notes and answer these

  1. 1.Without looking, explain variable and give one example or consequence.
  2. 2.Without looking, explain term and give one example or consequence.
  3. 3.Without looking, explain coefficient and give one example or consequence.
  4. 4.Without looking, explain collecting like terms and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

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