Expressions and variables

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


$$4\cdot x-3$$

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.


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


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


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

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