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 3×2, -(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. ‘3’ or ‘x’ or ‘z’.
A term can also be a number and a variable multiplied together.
E.g. ‘2a’ or ‘6y’ or ‘x2’ or ‘4xy’.
Equivalent expressions
Equivalent expressions are expressions which are the same, but look different.
For example the expression 3x+4y is equivalent to 4y+3x.
Algebraic Equations:
Algebraic equation is a statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.
Examples are x³ + 1 and (yx²+ 2xy – y)/(x – 1) = 12.