Adding Like Terms in Algebra
(KS3, Year 7)

The Lesson

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.

Question

Add the like terms below together.
3 x y plus x y

Step-by-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).

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.

3

Add the coefficients together.

3 plus 1 equals 4

4

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

4 x y

Answer:

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.

Question

Add the like terms below together.
a x y plus b x y

Step-by-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.

2

Identify the coefficients of the like terms.

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

3

Add the coefficients together.

a plus b

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

Answer:

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?

Lesson Slides

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. Open the slider in a new tab

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.
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See Also

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