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

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.  ‘$3$’ 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 $4y+3x$.