---
title: "Expanding Double Brackets"
description: "Expand products of two or more binomials, e.g., (x + 3)(x - 2) = x² + x - 6, using the grid method or FOIL; simplify the result by collecting like terms"
canonical: https://lightmysky.com/learn/mathematics/expanding-double-brackets-mt_KhS7K1Mgrw
source: https://lightmysky.com/learn/mathematics/expanding-double-brackets-mt_KhS7K1Mgrw.md
retrieved: 2026-10-19
---

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# Expanding Double Brackets

Expand products of two or more binomials, e.g., (x + 3)(x - 2) = x² + x - 6, using the grid method or FOIL; simplify the result by collecting like terms

Subject: Mathematics · Area: Algebra · Ages 13 to 14
Page: https://lightmysky.com/learn/mathematics/expanding-double-brackets-mt_KhS7K1Mgrw

## Ready when they can

- Expand the product of two binomials using a systematic method (grid or FOIL)
- Collect like terms after expansion to simplify the result
- Expand products involving negative terms correctly

## Lesson: Expanding Double Brackets

You already know how to expand a single bracket. Now there are two brackets, each with two terms. Every term in the first bracket has to multiply every term in the second bracket. That gives four small multiplications in total.

*(drawing: Think of it as a grid: 2 terms in the first bracket and 2 in the second. Every term meets every term, so you always get 4 multiplications.)*

**Example.** Expand (x + 3)(x - 2). First terms: x times x makes x squared. Outer terms: x times -2 makes -2x. Inner terms: 3 times x makes 3x. Last terms: 3 times -2 makes -6. Written out, that is x squared - 2x + 3x - 6.

FOIL just names the order: First, Outer, Inner, Last. It helps you remember all four multiplications so you never miss one. Any order works, as long as every term meets every term. A squared bracket such as (x + 1)² is two brackets, (x + 1)(x + 1), so you expand it the same way.

**Example.** Now collect like terms in x squared - 2x + 3x - 6. The -2x and 3x are like terms, so add them: -2x + 3x = x. The simplified answer is x squared + x - 6.

**Tip.** Watch the signs closely. In (x - 4)(x + 5): First is x squared, Outer is 5x, Inner is -4x, Last is -20. Collecting 5x - 4x gives x, so the answer is x squared + x - 20.

**Recap.** Multiply every term in the first bracket by every term in the second, then collect like terms to finish.

## Practice

16 questions on this page, each with its working shown.

## Needs first

- [Expanding Single Brackets](https://lightmysky.com/learn/mathematics/expanding-single-brackets-mt_FX4a2Q8XXN)
- [Collecting Like Terms](https://lightmysky.com/learn/mathematics/collecting-like-terms-mt_nNNVrLqPW3)
- [Adding and Subtracting Negative Numbers](https://lightmysky.com/learn/mathematics/adding-and-subtracting-negative-numbers-mt_qX7X7uMzsY)

## Opens up

- [Factorising Quadratics into Two Brackets](https://lightmysky.com/learn/mathematics/factorising-quadratics-into-two-brackets-mt_3QXgmWKfoA)
- [Algebraic Proof with Odd, Even and Consecutive Numbers](https://lightmysky.com/learn/mathematics/algebraic-proof-with-odd-even-and-consecutive-numbers-mt_p9bajOC17q)