# 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:

 Addition 4+y 4 plus y Subtraction x-5 x minus 5 8-a 8 minus a Division z/7 z divided by 7 14/x 14 divided by x Multiplication 9x 9 times x

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.

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

 $3^1$ 3 to the first power $3$ $4^2$ 4 to the second power or 4 squared $4 \cdot 4$ $5^3$ 5 to the third power or 5 cubed $5\cdot5\cdot5$ $2^6$ 2 to the sixth power $2\cdot2\cdot2\cdot2\cdot2\cdot2$

## Video lesson

Evaluate the expression when x=4 and y=3

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