Explanation:

In mathematics, an expression is a finite combination of symbols that are well-formed according to the rules applicable in the context at hand. Symbols can designate values (constants), variables, operations, relations, or can constitute punctuation or other syntactic entities.

In algebra an expression may be used to designate a value, which value might depend on values assigned to variables occurring in the expression; the determination of this value depends on the semantics attached to the symbols of the expression. (Our solved example in mathguru.com uses this concept)

These semantic rules may declare that certain expressions do not designate any value; such expressions are said to have an undefined value, but they are well-formed expressions nonetheless. In general the meaning of expressions is not limited to designating values; for instance, an expression might designate a condition, or an equation that is to be solved, or it can be viewed as an object in its own right that can be manipulated according to certain rules.

Many mathematical expressions include letters called variables. Any variable can be classified as being either a free variable or a bound variable.

For a given combination of values for the free variables, an expression may be evaluated, (Our solved example in mathguru.com uses this concept)

Although for some combinations of values of the free variables, the value of the expression may be undefined. Thus an expression represents a function whose inputs are the value assigned the free variables and whose output is the resulting value of the expression.

For example, the expression

x / y

evaluated for x = 10, y = 5, will give 2; but is undefined for y = 0.

http://en.wikipedia.org/wiki/Expression_(mathematics)

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