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”.
- Bi means two.
- 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.