Question

How do you classify expressions?

Answer 1

Hint: We have to be aware that in mathematics, an expression is built up from integer constants, variables, and the algebraic operations like addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number. Using this information, we will go ahead and classify them.

Complete step-by-step solution:
We know that an expression contains constants and variables that are coined together using operators like addition, subtraction, multiplication and division. Now, let us explore the types of expressions.
We can classify the expression in the following five categories - monomial, binomial, trinomial, polynomial, multinomial.
Now, let us have a look at each one of them.
1. Monomial: It is an algebraic expression which consists of one non-zero term only. We can write some examples of monomials:
b is a monomial in one variable b.
-12pq is a monomial in two variables p and q.
${h}^{2}$ is a monomial in one variable h.
2. Binomial: When we have an algebraic expression which consists of two non-zero terms, then it is called a binomial. We have the below examples for binomials:
a-b is a binomial in two variables a and b.
${h}^{2}+2hg$ is a binomial in two variables h and g.
3. Polynomial: An algebraic expression which consists of one, two or more terms is called a polynomial. Let us see the examples of polynomials:
4x+6y is a polynomial of two terms in two variables x and y.
$5{p}^{3}+2{p}^{2}-5p$ is a polynomial of three terms in one variable p.
4. Trinomial: If an algebraic expression of three non-zero terms only, then it is called a trinomial. We have examples of trinomial:
$7{a}^{2}-\dfrac{1}{2}a+5ab$ is a trinomial in two variables a and b.
6ab+4cd+e is a trinomial in five variables a, b, c, d and e.
5. Multinomial: An algebraic expression of two terms or more than three terms is called a multinomial. We have the examples of multinomial as:
$3s+6pq-4{a}^{2}+34p-9a$ is a multinomial of five terms in four variables a, p, q and s.

Note: Most often, students miss out to mention multinomial. So, they must remember that they must proceed according to the number of terms that an expression can have. We can consider multinomials as an extension of polynomials. The degree of a polynomial is defined as the highest degree of a monomial within a polynomial. Polynomials can be of any degree; there is no limit that degree of polynomial should lie under a certain value.