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How to Subtract Terms in Algebra (Mathematics Lesson)

Subtracting Terms in Algebra

Terms can be subtracted.

Imagine we wanted to subtract the term 2b from 3a.

3 a minus 2 b

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

Subtracting 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 subtracted by identifying the coefficients of the like terms and subtracting them from each other.

3 a minus 2 a

Don't forget: When the coefficient of a term is 1, there is no need to write it.

Read more about subtracting like terms in algebra

Subtracting Unlike Terms in Algebra

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

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

3 a and 2 b

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

Real Examples of How to Subtract Terms in Algebra

The following real examples show how to subtract 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 Subtract Like Terms in Algebra

An Example Question

Subtract the two terms below.

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

Subtract the coefficients from each other.

3 minus 2 equals 1
Step 4

Make the number found in Step 3 (1) the coefficient of the term (xy).

1 x y equals x y

We have subtracted the like terms together:

3xy - 2xy = xy

A Real Example of How to Subtract Unlike Terms in Algebra

An Example Question

Subtract the two terms below.

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 subtracted with the - operator. The subtractition cannot be simplified any further.

3xy - 2ab = 3xy - 2ab

Another Real Example of How to Subtract Terms in Algebra

Sometimes an expression will have both unlike and unlike terms.

In this case, subtract the like terms from each other and leave the unlike terms subtracted using the - operator. This simplifies the expression (the method is called collecting like terms).

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

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