Identifying parts in an algebraic expression

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

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.

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

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.