# Math Tutorial 12.3 - Binomial Expansion and Coefficients

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There are 6 lessons in this math tutorial covering Binomial Expansion and Coefficients. The tutorial starts with an introduction to Binomial Expansion and Coefficients and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of Binomial Expansion and Coefficients. you can access all the lessons from this tutorial below.

In this Math tutorial, you will learn:

• What are binomial expressions?
• What are the coefficients of binomial expressions?
• How do we expand binomial expressions at small powers?
• Why it is not suitable to use the FOIL Rule in higher power binomial expansions?
• What is Pascal's Triangle? What is/are its shape and features?
• What advantages and limitations does Pascal's Triangle have regarding the binomial coefficients?
• What does the Binomial Coefficient Theorem say?
• Why is Binomial Coefficient theorem more suitable to find the binomial coefficients of a binomial written in the expanded form?
• How do we expand other types of binomials that are not expressed in the standard form?

## Introduction

What is the expanded form of the binomial (a + b)2? What about (a + b)3? How did you find them?

Are you able to write the expanded form of (a + b)4? What about (a + b)5? How much time did this take to you?

Would you be happy to continue this procedure with (a + b)6, (a + b)7, etc.? Why/why not?

In previous chapters, you learned how to expand binomials up to the third power. These expansions are part of the eight special algebraic identities explained earlier. However, when it comes to higher powers, the procedure applied in those tutorials is not practical as it takes a lot of time to calculate the associated formulas. Therefore, it is necessary to find easier methods for expanding higher power binomials. In this tutorial, we will explain two methods that help you effortlessly write the expanded form of any binomials, in whatever power they may be.

Please select a specific "Binomial Expansion and Coefficients" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Sequences and Series Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
12.3Binomial Expansion and Coefficients
Lesson IDMath Lesson TitleLessonVideo
Lesson
12.3.1The Square and the Cube of a Binomial
12.3.2How to Expand Binomials in Higher Powers
12.3.3Using Pascal's Triangle
12.3.4Working with Binomial Coefficients and the Limitation of Pascal's Triangle
12.3.5The Binomial Coefficients Theorem
12.3.6What is a Binomial when it is not in the Standard Form

## Whats next?

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