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

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.

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

01

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

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

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

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

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

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

02

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

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

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

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

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

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

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

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