Expressions and variables
An algebraic expression comprises both numbers and variables together with at least one arithmetic operation.
Example
4⋅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⋅x−3
First we substitute x with 5
4⋅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⋅5⋅5=125
A power can also be written as
53=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.
53=5⋅5⋅5
| 31 |
3 to the first power | 3 |
| 42 |
4 to the second power or 4 squared | 4⋅4 |
| 53 |
5 to the third power or 5 cubed | 5⋅5⋅5 |
| 26 |
2 to the sixth power | 2⋅2⋅2⋅2⋅2⋅2 |
Evaluate the following expression when x=2 and y=−3,
x2−y+2x
(2)2−(−3)+2(2)=4+3+4=11.
10x+yx−y2
10(2)+(2)(−3)−(−3)2=20−6−9=20−15=5.
Video lesson
Evaluate the expression when x=4 and y=3
5x+y2−xy