An algebraic expression has one or more variables and can be written as a single term or as a sum of terms. Here are some examples of algebraic expressions.
In the examples above, is a single term, has two terms, has four terms, and has one term. In the expression , the terms and are called like terms because they have the same variables, and the corresponding variables have the same exponents. A term that has no variable is called constant term. A number that is multiplied by variables is called the coefficient of a term.
For example, in the expression, 2 is the coefficient of the term , 7 is the coefficient of the term , and -5 is a constant term.
The same rules that govern operations with numbers apply to operations with algebraic expressions. One additional rule, which helps in simplifying algebraic expressions, is that like terms can be combined by simply adding their coefficient as the following examples show.
A number or variable that is a factor of each term in an algebraic expression can be factored out, as the following examples show.
To multiply two algebraic expressions, each term of the first expression is multiplied by each term of the second expression, and the results are added, as the following examples show.
A statement of equality between two algebraic expressions that is true for all possible values of the variable involved is called an identity. All of the statement above are identities. Here are some standard identities that are useful.
A statement of equality between two algebraic expressions that is true for
only certain values of the variables involved is called an equation
. The values are called the solutions
of the equation. e.g.