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”.
- The meaning of Prefix “Bi” is two.
- 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
$(1) \,\,\,\,\,\,$ $a+b$
$(2) \,\,\,\,\,\,$ $x-2y$
$(3) \,\,\,\,\,\,$ $-\dfrac{p}{7}-\sqrt{3}pq^2r^3$
$(4) \,\,\,\,\,\,$ $-0.8m+m^2n^2$
$(5) \,\,\,\,\,\,$ $ut+\dfrac{1}{2}gt^2$