Types of Algebraic Expressions

Types of algebraic expressions may further be distinguished in the following five categories.

They are: monomial, polynomial, binomial, trinomial, multinomial.

1. Monomial: An algebraic expression which consists of one non-zero term only is called a monomial.

Examples of monomials:

a is a monomial in one variable a.

10ab2 is a monomial in two variables a and b.

5m2n is a monomial in two variables m and n.

-7pq is a monomial in two variables p and q.

5b3c is a monomial in two variables b and c.

2b is a monomial in one variable b.

2ax/3y is a monomial in three variables a, x and y.

k2 is a monomial in one variable k.


2. Polynomial: An algebraic expression which consists of one, two or more terms is called a polynomial.

Examples of polynomials:

2a + 5b is a polynomial of two terms in two variables a and b.

3xy + 5x + 1 is a polynomial of three terms in two variables x and y.

3y4 + 2y3 + 7y2 - 9y + 3/5 is a polynomial of five terms in two variables x and y.

m + 5mn – 7m2n + nm2 + 9 is a polynomial of four terms in two variables m and n.

3 + 7x5 + 4x2 is a polynomial of three terms in one variable x.

3 + 5x2 - 4x2y + 5xy2 is a polynomial of three terms in two variables x and y.

x + 5yz – 7z + 11 is a polynomial of four terms in three variables x, y and z.

1 + 2p + 3p2 + 4p3 + 5p4 + 6p5 + 7p6 is a polynomial of seven terms in one variable p.


3. Binomial: An algebraic expression which consists of two non-zero terms is called a binomial.

Examples of binomials:

m + n is a binomial in two variables m and n.

a2 + 2b is a binomial in two variables a and b.

5x3 – 9y2 is a binomial in two variables x and y.

-11p – q2 is a binomial in two variables p and q.

b3/2 + c/3 is a binomial in two variables b and c.

5m2n2 + 1/7 is a binomial in two variables m and n.


4. Trinomial: An algebraic expression of three non-zero terms only is called a trinomial.

Examples of trinomial:

x + y + z is a trinomial in three variables x, y and z.

2a2 + 5a + 7 is a trinomial in one variables a.

xy + x + 2y2 is a trinomial in two variables x and y.

-7m5 + n3 – 3m2n2 is a trinomial in two variables m and n.

5abc – 7ab + 9ac is a trinomial in three variables a, b and c.

x2/3 + ay – 6bz is a trinomial in five variables a, b, x, y and z.


5. Multinomial: An algebraic expression of two terms or more than three terms is called a multinomial.

Note: binomial and trinomial are the trinomials.

Examples of multinomial:

p + q is a multinomial of two terms in two variables p and q.

a + b + c is a multinomial of three terms in three variables a, b and c.

a + b + c + d is a multinomial of four terms in four variables a, b, c and d.

x4 + 2x3 + 1/x + 1 is a multinomial of four terms in one variable x

a + ab + b2 + bc + cd is a multinomial of five terms in four variables a, b, c and d.

5x8 + 3x7 + 2x6 + 5x5 - 2x4 - x3 + 7x2 - x is a multinomial of eight terms in one variable x.

These are the types of algebraic expressions explained with various types of examples.

Terms of an Algebraic Expression

Types of Algebraic Expressions

Degree of a Polynomial

Addition of Polynomials

Subtraction of Polynomials

Power of Literal Quantities

Multiplication of Two Monomials

Multiplication of Polynomial by Monomial

Multiplication of two Binomials

Division of Monomials







Algebra Page

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