In an algebraic expression, the objects separated by operation symbols (+, -, =, etc.) are referred to as terms. In the expression below,
2x2 - (x + 4)y + 3
2x2, (x + 4)y, and 3, are all terms. Expressions are made up of one or more terms, while equations are expressions that are separated by an equals sign.
Types of terms
The terms that make up an expression are most typically made up of a combination of constants, variables, and coefficients.
Constants are fixed quantities. They are well-defined quantities that do not vary, unlike variables. Examples of constants include numbers such as 0, 1, π, e, and more. π and e are two of the most widely used mathematical constants. Even though both π and e are irrational numbers, meaning that we can't express them as a ratio of two integers, they are still mathematical constants because their values, even if we can't write them explicitly, stay the same. π will always be the ratio of a circle's circumference to its diameter.
In generalized algebraic expressions or equations, constants are commonly denoted using "c," though other letters such as "k" are also used.
Variables are symbols used to represent unknown values. Some of the most commonly used symbols are x, y, z and t. Often, a variable may be named after the first letter of the object in question. For example, an unknown radius of a circle may be represented using the letter "r."
Variables are used as part of expressions to indicate a relationship between the terms of the expression or equation. For example, in the equation x = 3y, we don't know the value of x or y, but we know that x is 3 times of y because of the coefficient of 3, so if we knew either x or y, we could find the value of the other.
Coefficients are used in a number of areas of mathematics, but in algebra, a coefficient is a factor that a term in an algebraic expression is multiplied by. From the example above:
x = 3y
The coefficient of 3 multiplies the variable y, telling us that x is 3 times of y. In the equation
x = 3y + 3
the second 3 is a constant, not a coefficient, though technically we can think of the 3 as 3x0, in which case 3 would be the coefficient of x0.