A variable is a symbol that denotes a numerical quantity. Most variables are alphabetic characters. Algebra utilizes the concept of a variable to generalize mathematical concepts to a particular group of numbers, e.g. the set of real numbers. The number that the variable represents is called its value.
A constant is a symbol that represents a definite mathematical quantity. The most common examples of constants are the numerals used to represent real numbers, e.g., 3, 4.9, 2/3, etc. Symbols such as p and e are also constants, approximately denoting the values 3.141593 and 2.718282, respectively. Also, symbols that always represent the same quantity when used, such as g (acceleration due to gravity) or c (speed of light), are also called constants.
A term is a product with an unspecified number of factors, where the factors are variables or constants. The variables of a term are called literal factors, and the constants the numerical coefficient (or simply coefficient), of the term. Terms whose only factors are constants are called constant terms. Terms that have the same literal factors differ only in their numerical coefficients, and are called similar terms.
An algebraic expression is an additive combination of any number of terms.
By applying the distributive property, two or more similar terms can be combined into one term. The new term has the same literal factors as the similar terms, but its coefficient is the sum of the coefficients of the similar terms. This process is known as combining similar terms.
When each variable in an algebraic expression is replaced by a number, the algebraic expression takes on a numerical value. This process is known as evaluating algebraic expressions.
EX. In the algebraic expression 2x + 5ex2y2- p + 5.2x ; 2x, 5e x2y2, -p and 5.2x are the terms. -p is a constant, so it is also a constant term. The term 5ex2y2 has a coefficient of 5e and literal factors of x2y2 . Since the terms 2x and 5.2x have the same literal factor of x, they are similar terms.
The similar terms 2x and 5.2x can be combined into one term with literal factor x and coefficient equal to (2 + 5.2) = 7.2. The simplified expression is now 7.2x + 5ex2y2 - p. If we set x = 1 and y = 2, the expression is evaluated as
7.2(1) + 5e(12)(22) - p = 7.2 + 5e(4) - p = 58.4240
