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