What is important to know about Simplifying expressions?

Like terms have the same letter(s) and power(s): 3x and 5x are like terms; 3x and 3x² are not.

What is important to know about Simplifying expressions?

Collect like terms by adding or subtracting their coefficients.

What is important to know about Simplifying expressions?

When multiplying terms: multiply coefficients and add indices (e.g. 3x² × 2x³ = 6x⁵).

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Algebra · Foundation & Higher

Simplifying expressions

Simplifying algebraic expressions means collecting like terms and applying index laws. Like terms have exactly the same letters and powers and can be added or subtracted.

Revising simplifying expressions the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Simplifying expressions GCSE” on the site for the complete guide.

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Key facts to remember

1Like terms have the same letter(s) and power(s): 3x and 5x are like terms; 3x and 3x² are not.
2Collect like terms by adding or subtracting their coefficients.
3When multiplying terms: multiply coefficients and add indices (e.g. 3x² × 2x³ = 6x⁵).
4When dividing terms: divide coefficients and subtract indices (e.g. 6x⁵ ÷ 2x² = 3x³).
5An expression cannot be simplified further if all remaining terms are unlike.

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Worked examples

Example 1

Simplify 5x² + 3x − 2x² + 4x − 1

Working

Group like terms: (5x² − 2x²) + (3x + 4x) − 1
= 3x² + 7x − 1

Answer3x² + 7x − 1

Example 2

Simplify 4a²b × 3ab³

Working

Multiply coefficients: 4 × 3 = 12
Multiply a terms: a² × a = a³
Multiply b terms: b × b³ = b⁴
= 12a³b⁴

Answer12a³b⁴

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Common mistakes

✗Adding unlike terms (e.g. writing 3x + 2x² = 5x³).

✗Forgetting to carry the negative sign when collecting terms.

✗Adding indices when multiplying coefficients (e.g. 3x² × 2x = 6x² instead of 6x³).

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Exam tips

✓Underline or highlight like terms in different colours before collecting them.

✓With index laws: × means add indices, ÷ means subtract indices, power of a power means multiply indices.

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