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 nonzero term only is called a monomial.
Examples of monomials:
a is a monomial in one variable a.
10ab^{2} is a monomial in two variables a and b.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.
3y^{4} + 2y^{3} + 7y^{2}  9y + 3/5 is a polynomial of five terms in two variables x and y.3. Binomial: An algebraic expression which consists of two nonzero terms is called a binomial.
Examples of binomials:
m + n is a binomial in two variables m and n.
a^{2} + 2b is a binomial in two variables a and b.4. Trinomial: An algebraic expression of three nonzero terms only is called a trinomial.
Examples of trinomial:
x + y + z is a trinomial in three variables x, y and z.
2a^{2} + 5a + 7 is a trinomial in one variables a.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.
x^{4} + 2x^{3} + 1/x + 1 is a multinomial of four terms in one variable xThese are the types of algebraic expressions explained with various types of examples.
● Terms of an Algebraic Expression
Types of Algebraic Expressions
Multiplication of Two Monomials
Multiplication of Polynomial by Monomial
Multiplication of two Binomials
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