An algebraic expression of either sum or difference of two unlike terms is called a binomial.

Two unlike algebraic terms form a polynomial (algebraic expression). They are connected each other by either summation or difference to form an algebraic expression. Actually, two unlike terms form an algebraic expression to represent a quantity in algebraic form.

Bi is a prefix and its meaning is two and the meaning of nomial is unlike terms. Thus, the meaning of Binomial is two unlike terms. Hence, an algebraic expression is called as binomial if an algebraic expression is formed by two unlike algebraic terms to represent a quantity.

Observe the following four examples to understand how two unlike algebraic terms form binomials in algebra.

$a + b$

The terms $a$ and $b$ are two unlike algebraic terms. They are connected each other by summation to form an algebraic expression. The algebraic expression is having two unlike algebraic terms. Hence, it is known as a binomial.

$6x \,-\, \dfrac{3}{y}$

$6x$ and $\dfrac{3}{y}$ are two unlike algebraic terms and they are connected each other by minus sign ($-$) to form an algebraic expression. It contains two unlike algebraic terms. Therefore, the algebraic expression is called as a binomial.

$ -p^{\displaystyle 2}q + r$

The terms $–p^{\displaystyle 2}q$ and $r$ are two unlike terms and they connected by a plus sign ($+$) to form an algebraic expression. Hence, the algebraic expression is an example of a binomial.

$-3 \,-\, 7mno$

$-3$ and $7mno$ are two unlike algebraic terms and both of them are connected by difference to form an algebraic expression. Due to having two unlike algebraic terms in the expression, the expression is known as a binomial.

In this way, two unlike algebraic terms form binomials in algebra to represent quantities in algebraic form.

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