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.

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

Video lesson

Evaluate the expression when x=4 and y=3

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