Term

A term is an algebraic expression which can form a separable part of another expression such as an algebraic equation or a sequence. Terms are a specific part of the symbolic language of algebra. The symbols of this language were primarily developed during the sixteenth and seventeenth centuries and are used to represent otherwise lengthy expressions. They can be as simple as using the single character, +, to mean addition, or as complicated as y = 4x² + 2x - 3 to represent an algebraic polynomial equation.

In general, there are three types of algebraic expressions which can be classified as terms. These include expressions made up of a single variable or constant, ones that are the product or quotient of two or more variables and/or constants, and those that are the product or quotient of other expressions. For example, the number 4 and the variable x are both terms because they consist of a single symbol. The expression 2z is also a term because it represents the product of two symbols. It should be noted that terms like 2z, in which a number and a variable are written together, are indicated products because multiplication is implied. Therefore, the symbol 2z means 2 × z. Finally, an expression like 2pq(a + 5)n is a term because it represents a quotient (the result of division) of two expressions.

The symbols that make up a term are known as coefficients. In the term 4x, the number 4 is known as a numerical coefficient and the letter x is known as the literal coefficient. For this expression, we could say that 4 is the coefficient of x or x is the coefficient of 4.

Terms should be thought of as a single unit that represents the value of a particular number. This is particularly useful when discussing the terms of a larger expression such as an equation. In the expression 5x³ + 2x² + 4x - 7, there are four terms. Numbering them from left to right, the first term is 5x³, the second is 2x², the third is 4x, and the fourth is -7. Notice that the sign in front of a term is actually part of it.

Some expressions contain terms which can be combined to form a single term. These "like terms" contain the same variable raised to the same power. For example, the like terms in the expression 3x + 2x can be added and the equation simplifies to 5x. Similarly, the expression 7y² - 3y² can be simplified to 4y². Expressions containing unlike terms can not be simplified. Therefore, 4x² 2x is in its simplest form because the differences in the power of x prevents these terms from being combined.