What are Algebraic Expressions?
An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc. For example, let us have a look at the expression 5x + 7. Thus, we can say that 5x + 7 is an example of an algebraic expression. Here are more examples:
- 5x + 4y + 10
- 2x2y – 3xy2
- (-a + 4b)2 + 6ab
Variables, Constants, Terms, and Coefficients
There are different components of an algebraic expression. Let us have a look at the image given below in order to understand the concept of Variables, Constants, Terms, and Coefficients of any algebraic expression.
In mathematics,
- a symbol that doesn’t have a fixed value is called a variable. It can take any value. In the above example that involved matchsticks, n is a variable and in this case, it can take the values 1,2,3,… Some examples of variables in Math are a, b, x, y, z, m, etc.
- On the other hand, a symbol that has a fixed numerical value is called a constant. All numbers are constants. Some examples of constants are 3, 6, -(1/2), √5, etc.
- A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants by the operation of multiplication or division. Some examples of terms are 3x2, -(2y/3), √(5x), etc.
- Here, the numbers that are multiplying the variables are 3, -2/3, and 5. These numbers are called coefficients.
Algebraic terms
An algebraic term is either a single number or variable
E.g. ‘’ or ‘’ or ‘’.
A term can also be a number and a variable multiplied together
E.g. ‘’ or ‘’ or ‘’ or ‘’.
Equivalent expressions
Equivalent expressions are expressions which are the same, but look different. For example the expression is equivalent to .