Binomial

An expression that consists of two terms is called a binomial.

Introduction

The word “Binomial” is derived in English language from “Bi” and “Nomial”.

1. Bi means two.
2. Nomial means a term.

Bi is used as a prefix for the word “nomial” to form a word “binomial”. According to the meanings of them, the meaning of a binomial is two terms.

Two mathematical expressions are possibly connected by a plus sign $+$ or minus sign $-$. Then, it forms a mathematical expression, which consists of two terms. Therefore, the mathematical expression is called a binomial.

Examples

Binomials

$x^2$ and $xy$ are two mathematical expressions. Their sum or difference forms an expression as follows.

$(1).\,\,\,$ $x^2+xy$

$(2).\,\,\,$ $x^2-xy$

The above two mathematical expressions consist of two terms. Hence, each mathematical expression is called a binomial. Similarly, the following five mathematical expressions are also binomials.

$(1).\,\,\,$ $a+b$

$(2).\,\,\,$ $x-y$

$(3).\,\,\,$ $2x^2+3$

$(4).\,\,\,$ $y^4-\sqrt{3}y$

$(5).\,\,\,$ $z-7y^3$

Non-Binomials

Look at the following three mathematical expressions. They are not binomials.

$(1).\,\,\,$ $a$

$(2).\,\,\,$ $x^2-2y+3$

$(3).\,\,\,$ $\dfrac{3}{x+y}$

The first mathematical expression consists of only one term. Similarly, the second mathematical expression consists of more than two terms. So, they both are not binomials clearly.

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