24

Binomial Expansion

LEARNING OBJECTIVES

After studying this chapter, the student will be able to understand:

  • Binomial expansion
  • Binomial theorem
  • Characteristics of binomial expansion
  • General term of binomial expansion
  • Illustrations
  • Exercises

INTRODUCTION

The expression x + y, 2x + y, 3x − 4y, etc. are known as binomial expressions. Such expressions are represented as the sum or difference of two terms. When such binomial expressions are given with some index, the method of their expansions is known to us to some extent. For example,

(x + b)1 = x + b

(x + b)2 = x2 + 2bx + b2

(x + b)3 = x3 + 3x2b + 3xb2 + b3

(x + b)4 = x4 + 4x3b + 6x2b2 + 4xb3 + b4

These types of expansions are known as binomial expressions. If the index of binomial expression ...

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