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Like Terms in Algebra (Mathematics Glossary)

What Are Like Terms in Algebra?

A term is a collection of letters written together. An example of a term is shown below:

x y

Some terms will have the same combination of letters, but with a different sign or number in front of it. These are called like terms. The terms below are all like terms:

x y, 2 x y, minus 3 x y

A Real Example of Like Terms in Algebra

Terms can also include letters that have exponents (or powers).

The letter x has an exponent of 2 in the term below (x squared):

x squared y

Like terms will have the same combination of letters with the same exponent by each letter. The terms below are all like terms:

x squared y

A Definition of Like Terms in Algebra

Like terms are terms with the same variables (which have the same exponents). The only difference between like terms are the coefficients.

In this definition,

  • A term is a collection of numbers, letters and brackets all multiplied together. The letters may have exponents.

    2x2y is a term.
  • A variable is a letter that stands for a number. Its value is not fixed, its value can change.

    The x and y in 2x2y are variables.
  • An exponent tells you how many times a value is multiplied by itself.

    The 2 in 2x2y is an exponent.
  • A coefficient is a constant placed in front of the variables in the term.

    The 2 in 2x2y is a coefficient.

    A constant has a fixed value which does not change. It is often a number (like the 2 in our example).

    Constants can also be letters...

Like Terms in Algebra When Coefficients Are Letters

We have seen that like terms have the same combination of letters as each other. However, this is not strictly true.

Like terms must have the same combination of variables, which are always represented by letters (often x, y and z).

Like terms can have different coefficients. The coefficients are constants and are usually represented by numbers. But the coefficients can also be represented by letters (often a, b and c).

If a and b are constants and x and y are variables, the terms shown below are like terms:

a x y, b x y

Although they have a different combination of letters, they have the same combination of variables. Only the coefficients (the letters a and b) are different.

More Real Examples of Like Terms in Algebra

The following are all like terms:

  • Each is an x term, even though they have different coefficients.

    x, 3 x, minus 7 x
  • Each is an xy2 term, even though they have different coefficients.

    x y squared, 2 x y squared, half x y squared
  • Each is an (x + 1) term, even though they have different coefficients.

    x plus 1, 4 x plus 1, three quarters x + 1
  • All number terms are also like terms.

    1, 4, one quarter, minus 3

Read more about identifying like terms in algebra

Why Are Like Terms in Algebra Useful?

Like terms in algebra are useful because it can be used to simplify expressions.

The expression below has x and y terms:

x plus 2 y plus 5 x minus y

By identifying like terms, collecting them together and adding and/or subtracting them together, the expression can be simplified.

collect like terms

Read more about collecting like terms in algebra

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

Top Tip

Same Letters, Different Numbers...

In laymans terms, like terms have the same combination of letters. The only difference is the sign or number in front of the group of letters.

x y, 5 x y

...Except Where There Are Exponents...

Each letter in a like term must have the same exponent - the number that sits to the top-right of the letter.

x squared y, 5 x squared y

...And Except Where The Coefficient Are Letters

Sometimes a letter is used in the coefficient instead of a number. This is the only case where like terms have different letters - where the different letters are constants not variables.

x y, a x y

In this example, a is a constant, x and y are variables.