Identifying parts in an algebraic expression

Definition

An algebraic expression had different parts like, constants, terms, like terms, coefficients, and so on.

In this lesson, given an algebraic expression, we identify different parts as required.

For example, consider the following algebraic expression

6 + 4a + 9a + 10b

• 4a and 9a are like terms
• 6 is a constant
• 9 is a coefficient of term 9a
• 10b is a term
• 9a, 10b is a pair of unlike terms

Example 1

Identify the coefficient of p² in the expression:

9q + 8p 15p² 11r

Solution

Step 1:

The numeric part of a term is generally called the coefficient.

Step 2:

The term containing p² is 15p².

So, the coefficient of p² in the term is 15.

Example 2

Identify the like terms in the expression:

21x 13y 8x + 5y

Solution

Step 1:

The following are like terms because each term consists of variables, x, and a numeric coefficient.

21x, 8x

Step 2:

The following are like terms because each term consists of variables, y, and a numeric coefficient.

5y, 13y

Example 3

Identify the constant term in the expression:

10x + 51y + 18z + 69

Solution

Step 1:

In an algebraic expression, the term with no variables is called the constant.

Step 2:

In given expression, the constant is obviously 69.