Expanding Brackets for IGCSE Maths

What You Need to Know

Removing single and double brackets by multiplication. This subtopic is part of Algebra in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding expanding brackets is essential for achieving a strong grade in your IGCSE Maths exam.

Understanding Expanding Brackets

Expanding brackets means multiplying each term inside the bracket by the term outside. Single brackets: a(b+c) = ab+ac. Double brackets: (x+a)(x+b) = x²+(a+b)x+ab — use FOIL (First, Outer, Inner, Last). The perfect square (x+a)² = x²+2ax+a² and difference of two squares (x+a)(x−a) = x²−a² are key special cases. Expanding is the foundation for factorising, solving quadratics, and algebraic proofs in IGCSE 0580.

Step-by-Step Method

1. 1

   Single bracket

   Multiply every term inside by the term outside: 3(2x − 5) = 6x − 15. Watch the sign when multiplying by a negative: −2(x − 4) = −2x + 8.

2. 2

   Double brackets — FOIL

   First: x × x = x². Outer: x × b. Inner: a × x. Last: a × b. Add all four terms: (x+3)(x−5) = x² − 5x + 3x − 15 = x² − 2x − 15.

3. 3

   Collect like terms

   After expanding, add the two middle terms. Only x-terms combine with x-terms; constants combine with constants.

4. 4

   Perfect square shortcut

   (x+a)² = x² + 2ax + a². For (x+4)² = x² + 8x + 16. A common error is writing x² + 16 (forgetting the middle term).

5. 5

   Triple brackets

   Expand two brackets first, then multiply the result by the third bracket term by term.

Exam Tips for Expanding Brackets

• Never write (x+3)² = x² + 9 — the middle term 6x is worth a mark. Always use (a+b)² = a²+2ab+b².
• Expand brackets before collecting like terms — trying to do both simultaneously leads to sign errors.
• When multiplying by a negative, every sign inside changes: −2(3x − 4) = −6x + 8, not −6x − 8.
• In show-that/proof questions, expand fully and show every term before simplifying — all working must be visible.

Practice Questions

Frequently Asked Questions