Skip to main content
MathidiaMathematics Academy
Advanced algebraic manipulation
Lesson 11 of 75
Introduction

Expanding several brackets

Objective. Expand products involving three linear factors methodically.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Expanding several brackets means multiplying out three or more linear factors step by step, never all at once. The reliable method is to expand two brackets first using the grid or FOIL method, then multiply the resulting quadratic by the remaining bracket term by term. For example, (x + 1)(x + 2)(x + 3) first expands to (x² + 3x + 2)(x + 3), then each term of the quadratic multiplies every term of the linear bracket. Always collect like terms carefully at each stage to avoid losing terms.

Worked example

Expand and simplify (x + 2)(x − 1)(x + 3) fully as a cubic expression.

2 … 1
Illustrated card showing 2 … 1
  1. 1Expand the first two brackets: (x + 2)(x − 1) = x² + x − 2.
  2. 2Multiply this quadratic by (x + 3) term by term.
  3. 3x² × (x + 3) = x³ + 3x², x × (x + 3) = x² + 3x, −2 × (x + 3) = −2x − 6.
  4. 4Collect like terms: x³ + 4x² + x − 6.

Answer: x³ + 4x² + x − 6

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils try to expand all three brackets simultaneously and miss cross terms, especially the constant-times-constant term. Always expand two brackets completely first, then multiply by the third.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard