# Multinomials

An algebraic expression that contains at least two terms is called a multinomial.

## Introduction

The meaning of multinomial is defined from a prefix “Multi” and a Latin term “Nomial”.

1. The meaning of prefix “Multi” is more than one or many.
2. The meaning of “Nomial” is a term.

As per the meanings of both terms, the meaning of a multinomial is defined as an algebraic expression with more than one term. It is actually defined to represent a quantity in mathematical form by two or more unlike terms.

In a multinomial, two or more unlike terms are connected mathematically by either plus or minus or both signs for expressing an algebraic expression in mathematical form. It is also called as a polynomial of two or more terms and it is originally formed in two different ways in algebra.

Except monomial, all polynomials like binomial, trinomial, quadrinomial and so on are best examples for multinomials.

### More than One Term

A multinomial is purely formed by two or more unlike algebraic terms.

#### Examples

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

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

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

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

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

### One or more terms and a Number

A multinomial is also formed by a number and one or more algebraic terms.

##### Examples

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

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

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

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

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

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