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How to Add Like Terms in Algebra (Mathematics Lesson)

Adding Like Terms in Algebra

Like terms can be added.

Imagine we wanted to add 3xy and xy.

3 x y plus x y

How to Add Like Terms in Algebra

Adding like terms is easy. Add the coefficients of the like terms together.

An Example Question

Add the like terms below together.

3 x y plus x y
Step 1

Check that the terms are like terms.

3xy and xy are like terms.

  • They have the same variables: x and y.

  • Each variable has the same exponent: x and y both have no exponents (actually an explicit exponent of 1).

  • The only difference is the coefficient: 3xy has a coefficient of 3, xy has no coefficient (actually an explicit coefficient of 1).

Step 2

Identify the coefficients of the like terms.

3 x y has a coefficient of 3, x y has a coefficient of 1

Don't forget: A coefficient is the constant (usually a number) in front of a term. If a letter does not have a number in front of it, its coefficient is 1.

Step 3

Add the coefficients together.

3 plus 1 equals 4
Step 4

Make the number found in Step 3 (4) the coefficient of the term (xy).

4 x y

We have added the like terms together:

3xy + xy = 4xy

How to Add Like Terms in Algebra When the Coefficients Are Letters

Coefficients can be letters as well as numbers.

By convention, the letters a, b, c are used to represent constants (such as coefficients) whereas x, y, z are used for variables.

An Example Question

Add the like terms below together.

a x y plus b x y
Step 1

Check that the terms are like terms.

axy and bxy are like terms.

  • They have the same variables: x and y.

  • Each variable has the same exponent: x and y both have no exponents (actually an explicit exponent of 1).

  • The only difference is the coefficient: axy has a coefficient of a, bxy has a coefficient of b.

Step 2

Identify the coefficients of the like terms.

a x y has a coefficient of a, b x y has a coefficient of b
Step 3

Add the coefficients together.

a plus b
Step 4

Make the term found in Step 3 (a + b) the coefficient of the term (xy).

 open bracket a plus b close bracket x y

We have added the like terms together:

axy + bxy = (a + b)xy

Real Examples of How to Add Like Terms in Algebra

More real examples of how to add like terms in algebra are given below:

examples of adding like terms

Can you see that the coefficients have been added in each case?

Another Real Example of How to Add Like Terms in Algebra

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

The example shows that the same method can be used when coefficients are numbers and letters.

Curriculum
Algebra Lessons
Interactive Test
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Here's a second test on adding like terms.
Here's a third test on adding like 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.