# Expressions and variables

An algebraic expression comprises both numbers and variables together with at least one arithmetic operation.

Example:

$\\ 4\cdot x-3 \\$

A variable, as we learned in pre-algebra, is a letter that represents unspecified numbers. One may use a variable in the same manner as all other numerals:

To evaluate an algebraic expression you have to substitute each variable with a number and perform the operations included.

Example:

Evaluate the expression when x=5

$\\ 4\cdot x-3 \\$

First we substitute x with 5

$\\ 4\cdot 5-3 \\$

And then we calculate the answer

$\\ 20-3=17 \\$

An expression that represents repeated multiplication of the same factor is called a power e.g.

$\\ 5\cdot 5\cdot 5=125 \\$

A power can also be written as

$\\ 5^3=125 \\$

Where 5 is called the base and 3 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

$\\ 5^3=5\cdot 5\cdot 5 \\$

Videolesson: Evaluate the expression when x=4 and y=3

$\\5x + y^{2}- xy \\$