An algebraic expression has a wide definition. It is broadly defined as a set consisting of variables, constants and algebraic operators. A single element or all possible combinations of the elements in such a set give rise to different types of expressions. Hence examples of algebraic expression will help to understand the clear meaning of algebraic expression.
Example of an algebraic expression
A mathematical statement consisting variables, constants and the inter related algebraic operations is defined as an algebraic expression. Since there is no condition on the number of variables, constants or the number of operations, an algebraic expression can be in any form. It will be easier to understand by classifying all possible types of algebraic expressions with an example in each case.
Example by number of terms
The number of terms in an expression is used as a key word to identify. An expression with a single term is called ‘monomial expression’. For example ‘x’ is a monomial algebraic expression. An expression with two terms is called ‘binomial expression’. ‘x + a’ is an example of a binomial algebraic expression, where ‘a’ could be a variable or constant. An expression with three terms is called ‘trinomial expression’. As an example, we can say ‘x + y + z’ is a trinomial algebraic expression. Algebraic expressions consisting more than three terms are generally termed as ‘polynomial algebraic expression’. For example, ‘x + y + z + a’ is a polynomial algebraic expression.
Example by degree of terms
Expressions are also classified according to the highest degree (meaning the power) found in any of the terms. As an example, ‘x2
+ 2x + 4’ is an algebraic expression of degree 2 , because the first term has the maximum degree of 2. It may be noted that ‘xy + 2x + 4’ is also an example of an algebraic expression of degree 2. In this case, the highest power is determined by the sum of the power of each variable in the first term.
It makes more sense when an algebraic expression is described jointly by the number of terms and the degree. For example describing ‘x2
+ xy + z’ as a trinomial algebraic expression of degree 2 is more eminent.
As a special example, a single degree trinomial with two variables and a constant is called a linear algebraic expression. Similarly a second order trinomial with a single variable and a constant is called quadratic expression.
In case the highest degree of the variable in an expression is a fraction, that is, if the variable is inside a radical symbol, then it is called as an radical expression. For example, (√x) + 2 is a radical expression.
Other examples of algebraic expressions
When there is a constant exponent for a single variable is called power expression. To cite an example, xa
where ‘a’ is a constant, is a power expression. On the other hand if the variable is in exponent’s place to a constant, the algebraic expression is called an exponential expression. For example, ax
where ‘a’ is a constant, is an exponential expression.
When an algebraic expression is a logarithm of a variable to any base is called as logarithmic expression. As an example, logb
(x) is a logarithmic expression.