# Multinomial

An expression that contains two or more algebraic terms is called a multinomial.

## Introduction

The true meaning of multinomial as per English language is an expression which consists of at least two unlike terms.

A quantity cannot be always expressed in the form a term. In such cases, two or more unlike algebraic terms are connected together by either subtraction or addition or both form. Hence, the algebraic expressions are called multinomials in algebraic mathematics.

### Examples

Multinomials are actually formed by the interconnection of unlike terms with either positive $(+)$ and negative $(-)$ signs in mathematics.

01

#### Unlike Algebraic Terms

A multinomial can be formed by the interconnection of two or more unlike algebraic terms purely.

##### Examples

$(1) \,\,\,\,\,\,$ $a+4b$

$(2) \,\,\,\,\,\,$ $m-mn+mno$

$(3) \,\,\,\,\,\,$ $p^2$ $-\sqrt{7}q^2$ $-4r^2$ $-s^2$

$(4) \,\,\,\,\,\,$ $-u$ $+\dfrac{4}{5}u^5t$ $-ut^2$ $+u^2t^2$ $-5u^2t^3$

$(5) \,\,\,\,\,\,$ $2x$ $+y$ $+6xy$ $-x^2y$ $-0.175xy^2$ $+x^2y^3$

02

#### Combination of Terms and a Number

A multinomial can also formed by the interconnection of the combination of a number and at least an algebraic term.

##### Examples

$(1) \,\,\,\,\,\,$ $x-5$

$(2) \,\,\,\,\,\,$ $a^2-b^2+0.15$

$(3) \,\,\,\,\,\,$ $m$ $-\sqrt{5}m^2$ $-m^3$ $-2$

$(4) \,\,\,\,\,\,$ $p^3$ $+\dfrac{8}{3}p^2q$ $-pq^3$ $-pq$ $+6$

$(5) \,\,\,\,\,\,$ $j^2$ $+3j^3$ $+4j^4k$ $-8j^5$ $+0.9j^6$ $+3j^7$ $-10$

The examples are binomials, trinomials and so on. Hence, a multinomial can be a binomial or trinomial and so on.