Suppose Shyam and Ghanshyam are two brothers. Assume Shyam has three marbles more than Ghanshyam. The total number of marbles is 20. Now, can we determine the exact number of marbles that Shyam has? Obviously, the answer is no. The reason is that we don’t know the exact number of marbles any brother has. We only have the information that Shyam has three more marbles than Ghanshyam.

To find out the exact number of marbles that Shyam or Ghanashyam has, we can make use of an algebraic equation. In other words, we will try to express the information in the form of mathematics and try to understand the number of marbles owned by both of them.

To start with let us assume that Ghanshyam has X number of marbles. Now according to the information, Shyam has three more marbles than Ghanashyam. Hence, the number of marbles that Shyam has can be expressed through an algebraic equation: x+3. The total number of marbles owned by them is 20.

Hence, we can put the entire information in the form of mathematics through an algebraic equation.

A certain times, an equation may or may not have a constant.

Understanding a Variable, Operator, and Constant.

Variable: A variable is an unknown quantity that has to be found out. It is expressed using alphabets or symbols. You can use alphabets such as X, Y, Z or A, B, C or P, Q, R.

Operator: Operator is nothing but addition, subtraction, division, or multiplication.

Constant: Constant is a number that comes after the operator.

Coefficient of a term: Let us constopicIder an equation 2X + Y. Here, 2 is the coefficient of the unknown variable X. Thus, the number of a variable term is called the coefficient of the variable.

Definition of algebraic expression: An algebraic expression is usually expressed in the form of an equation having variables, coefficient of variables, integer constants, and algebraic operations such as addition, multiplication, subtraction, and division.

Please note: A variable can have an exponential component. For example, we can have an equation in the form of: x^2 + 2x + 1 = 0

In this case, the symbol ^ denotes power or raise to a variable x. This is called a quadratic equation.

Examples of algebraic expression:

Let us take more examples to understand algebraic expressions.

Example 1:

2x+7=0

Here too is the coefficient of the variable X and 7 is the constant.

Example 2:

x^3 + 2x + 1 

In this case, 3 is the power of the term x^3 and 2 is the coefficient of variable X while number 1 is the constant.

Example 3:

2x^3 + x^2 + 3x + 1 = 0

In the above example, 2x^3 is the first term. Here, 3 is the power of the variable X and two is the coefficient of the term x^3. 

x^2 is the second term. In this case, two is the power of variable X.

ConstopicIdering 3x, 3 is the coefficient of the variable X. 

Number 1 is the constant.