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 Description  
 Algebraic Expression:  A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.
Examples of Algebraic Expressions
In an algebraic expression, the variable represents values of a quantity that can vary. We need to define what the variable represents.

For example, suppose we wanted to write an expression to find the total cost of movie tickets for different groups of people, given that tickets cost $5 each. We can define the variable "P" to represent the number of people in a group. Then the algebraic expression

5 x P or 5P

represents the total cost of movie tickets for a group of P people. So, if our group has 3 people in it, we can substitute into our algebraic expression to find the total cost of movie tickets is

5 x 3, or 15 dollars.

Suppose we wanted to write an expression to find the perimeter of the figure below:



We know the length is equal to 75, but the width is not known. We can define "w" to be the width, so that our algebraic expression for the perimeter is

w + w + 75 + 75, which simplifies to 2w + 150

Non-Example of Algebraic Expressions
The expression 550 + 20 is not an algebraic expression because it does not contain at least one variable.

We also distinguish between an algebraic expression and an algebraic equation. An equation consists of two algebraic expressions and an equal sign. An example of an algebraic equation is shown below.

10x + 3 = 8x - 7

Interesting to Note:

Some historians claim that our word "algebra" comes from a book written by al-Khowarizmi, an Arabian mathematician. The title of the book was al-jabr w'al-muqabalah, which means opposition (al-jabr) and restoration (al-muqabalah). So, we may say that al-jabr means to "add the opposite" and al-muqabalah means to "combine your like terms".