How to Identify Like Terms in Algebra

Identifying Like Terms in Algebra

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:

x plus 3 x squared y plus 3 x minus half x squared y

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 plus 3 x squared y plus 3 x minus half x squared y

In this example, we can see that there are x terms and x2y terms.

x terms

The x and 3x terms look like they are like terms.

x terms highlighted

Let's check the x terms:

Step-by-Step:

1

Check that the same variables appear in both terms.

x

3x

The variable x appears in both terms.

2

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

x = x1

3x = 3x1

There is no exponent by each 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.

x = 1x

3x

There is no coefficient in front of the 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.

x2y terms

The 3x2y and −½x2y terms look like they are like terms.

x squared y terms highlighted

Let's check the x2y terms:

Step-by-Step:

1

Check that the same variables appear in both terms.

3x2y

−½x2y

The variable x and y appear in both terms.

2

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

3x2y = _3x2y1

−½x2y = -½x2y1

The 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.

3x2y

−½x2y

The coefficient of the 3x2y term is 3. The coefficient of the −½x2y term is −½.

This is the only difference between each of the like terms.

Answer:

3x2y and −½x2y are like terms.

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See Also

What is algebra? What is a like term? What is a variable? What is an exponent? What is a coefficient? What is a constant?