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How to Subtract Like Terms in Algebra (Mathematics Lesson)

Subtracting Like Terms in Algebra

Like terms can be subtracted.

Imagine we wanted to subtract xy from 3xy.

3 x y minus x y

How to Subtract Like Terms in Algebra

Subtracting like terms is easy. Subtract the coefficients of the like terms from each other.

An Example Question

Subtract the like terms below from each other.

3 x y minus 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 has 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

Subtract the coefficients from each other.

3 minus 1 equals 2
Step 4

Make the number found in Step 3 (2) the coefficient of the term (xy).

2 x y

How to Subtract 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

Subtract the like terms below from each other.

Step 1

Check that the terms 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

Subtract the coefficients from each other.



Step 4

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

open bracket a minus b close bracket x y

We have subtacted the like terms from each other:

axy - bxy = (a - b)xy

Real Examples of How to Subtract Like Terms in Algebra

More examples of how to subtract like terms in algebra are given below.

examples of subtracting like terms

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

Another Real Example of How to Subtract Like Terms in Algebra

The slider below shows a real example of how to subtract 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 subtracting like terms.
Here's a third test on subtracting 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.