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.

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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.

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● 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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