Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Simplifying Algebraic Expressions — collecting like terms, expanding brackets and applying index laws — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Simplifying Algebraic Expressions in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Simplifying Algebraic Expressions revision-guide angle, while Tutopiya’s Simplifying Algebraic Expressions subtopic page owns the learning resource and the free Simplifying Algebraic Expressions quiz owns the practice.

Simplifying Algebraic Expressions is core Algebra in Cambridge IGCSE Mathematics (0580/0607). Before you can solve equations or factorise, you must be able to collect like terms, expand single and double brackets, and combine expressions without sign slips. Examiners test this in direct “simplify” questions and as the first step in longer problems. This guide explains the subtopic, exam wording, and where to practise.

Key takeaways

• Like terms share the same variable part — 3x and 5x are like terms; 3x and 3x² are not.
• Expanding means multiply every term inside the bracket by the term outside.
• Double brackets use FOIL or the grid method: (a + b)(c + d) = ac + ad + bc + bd.
• Simplifying feeds into Factorisation and Linear Equations and Inequalities.

What is Simplifying Algebraic Expressions in Cambridge IGCSE Maths?

Simplifying an algebraic expression means writing it in the shortest equivalent form by collecting like terms and removing unnecessary brackets. In Cambridge IGCSE Mathematics, this includes adding/subtracting expressions, expanding single brackets (3(2x − 1)), double brackets ((x + 2)(x − 3)), and simplifying with index laws. It is procedural but unforgiving — one sign error ruins the whole answer.

Read the full explanation on Tutopiya’s Simplifying Algebraic Expressions subtopic page before you attempt questions.

The core techniques you must master

Technique	Rule	Example
Collect like terms	Add/subtract coefficients of same variable	4x + 3 − 2x + 5 = 2x + 8
Expand single bracket	Multiply each term inside	3(2x − 4) = 6x − 12
Expand double brackets	Multiply each term in first by each in second	(x + 1)(x + 2) = x² + 3x + 2
Subtract expressions	Distribute the minus to every term	5x − (2x − 3) = 5x − 2x + 3 = 3x + 3

How to simplify — step by step

1. Expand all brackets first — single then double.
2. Collect like terms — group x terms, y terms and constants separately.
3. Apply index laws if powers appear — x² × x³ = x⁵.
4. Write terms in standard order — highest power first, e.g. 2x² + 3x − 1.
5. Check signs especially when subtracting a bracket.

Test yourself with the free Simplifying Algebraic Expressions quiz.

Expanding double brackets: patterns to recognise

Pattern	Result	Example
(x + a)(x + b)	x² + (a+b)x + ab	(x + 3)(x + 2) = x² + 5x + 6
(x + a)(x − a)	x² − a² (difference of squares)	(x + 5)(x − 5) = x² − 25
(x + a)²	x² + 2ax + a²	(x + 4)² = x² + 8x + 16

Simplifying in past-paper wording: command words that matter

Command word / phrase	What the question wants	Typical stem
Simplify	Shortest equivalent expression	”Simplify 3(2x − 1) + 2(x + 4).”
Expand and simplify	Expand brackets then collect terms	”Expand and simplify (x + 3)(x − 2).”
Write in its simplest form	Fully simplified	”Write (2x²)³ in its simplest form.”
Show that	Prove equivalence with working	”Show that (x + 2)² − (x − 2)² = 8x.”
Work out	Calculate simplified result	”Work out the simplified expression.”

Worked exam-style stems (how to answer the wording)

1. “Simplify 4(2x − 3) − 2(x + 5).” Expand: 8x − 12 − 2x − 10. Collect: 6x − 22. Reward: minus distributed to both terms in second bracket.
2. “Expand and simplify (2x + 1)(x − 4).” 2x² − 8x + x − 4 = 2x² − 7x − 4. Reward: four products from FOIL; like terms collected.
3. “Show that (x + 3)(x − 3) = x² − 9.” Expand left side: x² − 3x + 3x − 9 = x² − 9. Reward: full expansion before conclusion.

Work similar stems on the Algebra topical past paper questions and the Simplifying Algebraic Expressions quiz.

How Simplifying connects to the rest of Algebra

Expanded forms reverse into Factorisation. Simplified expressions are solved in Linear Equations and Inequalities. Substitution is easier when expressions are simplified first. Use the Cambridge IGCSE Maths resource hub for the full unit.

Common mistakes students make

• Treating 3x and 3y as like terms — they are not.
• Forgetting to multiply every term inside the bracket.
• Sign error when subtracting a bracket: 5 − (x − 2) written as 5 − x − 2 instead of 5 − x + 2.
• Stopping before fully collecting all like terms.

When you need more support

If expanding double brackets keeps failing, work through the Factorisation quiz (reverse practice helps) and the Algebra topical past paper questions, then get help from a Cambridge IGCSE Maths tutor.

Frequently asked questions

What are like terms? Terms with exactly the same variable combination — same letters, same powers. 4xy and −2xy are like terms; 4x and 4x² are not.

Do I need to know the difference of squares? Yes — (a + b)(a − b) = a² − b² appears frequently and speeds up expansion.

Is expanding the opposite of factorising? Yes. Expanding removes brackets; factorising puts brackets back in. Knowing both directions strengthens each skill.

How do I revise Simplifying Algebraic Expressions effectively? Practise ten single-bracket and ten double-bracket questions, then take the Simplifying Algebraic Expressions quiz.

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Start with the Simplifying Algebraic Expressions subtopic page, then book a free trial with a Cambridge IGCSE Maths specialist.

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