Binomials

An algebraic expression that contains two terms is called a binomial.

Introduction

The meaning of binomial is defined from a prefix “Bi” and a Latin term “Nomial”.

1. The meaning of Prefix “Bi” is two.
2. The meaning of “Nomial” is a term.

Combining the meanings of both terms, the term binomial is defined in algebra as an algebraic expression with two terms. A binomial is actually expressed in terms of two unlike algebraic terms for representing a quantity mathematically. In a binomial, the two unlike algebraic terms are connected by plus ($+$) or minus sign ($-$) to form an algebraic expression.

A binomial is also known as a polynomial of two terms. It is possibly formed in two different forms.

A term and a Number

The binomials are formed by two unlike terms but in some cases, one term is an algebraic term and other term is a number.

Examples

$(1) \,\,\,\,\,\,$ $2b+5$

$(2) \,\,\,\,\,\,$ $x-7$

$(3) \,\,\,\,\,\,$ $-\dfrac{3}{2}+0.75xy^2$

$(4) \,\,\,\,\,\,$ $-pqr-8$

$(5) \,\,\,\,\,\,$ $r^3+7\sqrt{6}$

Two Unlike Algebraic terms

Similarly, the binomials are also formed purely by two unlike algebraic terms.

Examples

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

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

$(3) \,\,\,\,\,\,$ $-\dfrac{p}{7}-\sqrt{3}pq^2r^3$

$(4) \,\,\,\,\,\,$ $-0.8m+m^2n^2$

$(5) \,\,\,\,\,\,$ $ut+\dfrac{1}{2}gt^2$

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