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How to Add Terms in Algebra (Mathematics Lesson)

Adding Terms in Algebra

Terms can be added.

Imagine we wanted to add the terms 2a and 3b.

2 a plus 3 b

The method for adding terms depends on whether the terms are like or unlike.

Adding Like Terms in Algebra

Like terms have the same variables (letters), each with the same exponents by them. The only difference is their coefficient (the number, or sometimes the letter, in front of them).

2a and 3a are like terms. They have the same letters (a), with the same exponents. The only difference is 2a has a coefficient of 2 while 3a has a coefficient of 3.

2 a and 3 a

If terms are like terms, the terms are added by identifying the coefficients of the like terms and adding them together.

2 a plus 3 a

Read more about adding like terms in algebra

Adding Unlike Terms in Algebra

Unlike terms have different variables (letters) or different exponents.

2a and 3b are unlike terms. They have different variables (a in one, b in the other).

2 a and 3 b

If terms are unlike, the terms are simply added using the + operator. The expression cannot be simplified any further.

2 a plus 3 b

Real Examples of How to Add Terms in Algebra

The following real examples show how to add terms in algebra.

The method is slightly different depending on whether the terms are unlike or like, so the first step is always to identify whether terms are like or unlike.

A Real Example of How to Add Like Terms in Algebra

An Example Question

Add the two terms below.

3 x y plus 2 x y
Step 1

Check whether the terms are unlike or like.

In our example, the terms are like. They have the same variables (x and y), with the same exponents. The only difference is 3xy has a coefficient of 3 while 2xy has a coefficient of 2.

3 x y and 2 x y are like terms

Step 2

Identify the coefficients of the terms.

3 x y has a coefficient of 3. 2 x y has a coefficient of 2
Step 3

Add the coefficients together.

 3 plus 2 equals 5
Step 4

Make the number found in Step 3 (5) the coefficient of the term (xy).

5 x y

We have added the like terms together:

3xy + 2xy = 5xy

A Real Example of How to Add Unlike Terms in Algebra

An Example Question

Add the two terms below.

3 x y plus 2 a b
Step 1

Check whether the terms are unlike or like.

In our example, the terms are unlike. They have different variables (x and y in one, a and b in the other).

3 x y and 2 a b are unlike terms

Step 2

Leave the terms added with the + operator. The expression cannot be simplified any further.

We have added the like terms together:

3xy + 2ab = 3xy + 2ab

Another Real Example of How to Add Terms in Algebra

Sometimes an expression will have both unlike and unlike terms.

In this case, add the like terms together and leave the unlike terms added using the + operator. This simplifies the expression (the method is called collecting like terms).

The slider below shows a real example of how to add terms in algebra.

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Here's a second test on adding terms.
Here's a third test on adding terms.

Note

What Is a Like Term in Algebra?

Like terms are terms with the same combination of letters (and/or brackets).

The only difference is the sign or number in front of the group of letters.

Each letter (and/or bracket) in a like term must have the same exponents - the number that sits to the top-right of the letter.

What Is a Term in Algebra?

A term is a collection of numbers, letters and brackets all multiplied together.

Terms are separated by + or - signs in an algebraic expression.