## The Lesson

Like terms are terms with the same variables (which have the same exponents). The only difference between like terms are the coefficients. Like terms are useful because we can collect like terms to simplify expressions in algebra. Before we can collect like terms, we must be able to identify them. Imagine we wanted to identify the like terms in the expression below:## How to Identify Like Terms in Algebra

Identifying like terms is easy. Look for terms that have the same collection of letters, with the same exponent (or power) next to them. It is useful to know how to check for like terms:- Check that the same variables (letters) appear in each of the terms.
- Check that the exponent of each variable is the same in each of the terms.
- Check that the only difference between the like terms is the coefficient. This is normally the number in front of the term, although a coefficient can sometimes be a letter (a constant).

## Question

Identify the like terms in the expression below.**x**terms and

**x**terms.

^{2}y__x terms__

The **x**and

**3x**terms look like they are like terms. Let's check the

**x**terms:

## Step-by-Step:

# 1

Check that the same variables appear in both terms.
The variable

**x**

3**x**

**x**appears in both terms.# 2

Check that the exponent of each variable is the same in each of the terms.
There is no exponent by each

x = x^{1}

3x = 3x^{1}

**x**in each of the terms. (Actually, the exponent is**1**but there is no need to write it).# 3

Check that the only difference between the like terms is the coefficient.
There is no coefficient in front of the

x = **1**x

**3x**

**x**term. (Actually, the coefficient is**1**but there is no need to write it). The coefficient of the**3x**term is**3**. This is the only difference between each of the like terms.## Answer:

**x**and

**3x**are like terms.

__x__^{2}y terms

The ^{2}y terms

**3x**and

^{2}y**−½x**terms look like they are like terms.

^{2}yLet's check the

**x**terms:

^{2}y## Step-by-Step:

# 1

Check that the same variables appear in both terms.
The variable

3**x**^{2}**y**

−½**x**^{2}**y**

**x**and**y**appear in both terms.# 2

Check that the exponent of each variable is the same in each of the terms.
The

3x** ^{2}**y = _3x

**y**

^{2}

^{1}−½x** ^{2}**y = -½x

**y**

^{2}

^{1}**x**has an exponent of**2**in each of the terms. There is no exponent for the**y**in each of the terms. (Actually, the exponent is**1**but there is no need to write it).# 3

Check that the only difference between the like terms is the coefficient.
The coefficient of the

**3**x^{2}y

**−½**x^{2}y

**3x**term is^{2}y**3**. The coefficient of the**−½x**term is^{2}y**−½**. This is the only difference between each of the like terms.## Answer:

**3x**and

^{2}y**−½x**are like terms.

^{2}y