Polynomials (many terms) are algebraic expressions formed by adding or subtracting monomials (single terms with positive exponents or constants). A Binomial is a polynomial containing two terms, bi meaning two.

In terms of nomenclature, 'bi' means 2 hence binomial means two terms. So in general, a binomial is a polynomial containing two terms. The general form can be written as axn ± bym
A different and simpler way of defining a binomial is that it is an algebraic expression containing two terms connected by a sum of a difference sign. Example: 3x+5y,a+3x, x2-3x…etc.

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

Examples:

2x -3 This binomial is formed by subtracting 3 from 2x.
x2 + 4y2 The term 4y2 is added to x2 to give a Binomial expression.
The product of many variables yield only monomials
3xyz has three variables namely x, y and z but it is a single term or a monomial. The constant 3 is the coefficient of the term xyz.

More examples for Binomials:
5abc + 6xy
ax + by
$\frac{x^3}{3}$+ $\frac{y^2}{2}$

The verbal expressions are often expressed as Binomials.

Verbal Expressions Algebraic Expression
Three more than a number x + 3
Five added to square of a number z2 + 5
The length of a rectangle is 4 less
than twice the width
2w - 4
Dan's age is ten less than half his father's age $\frac{x}{2}$ - 10
sum of the squares on the legs of a right triangle a2 + b2