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:
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:
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):
Like terms will have the same combination of letters with the same exponent by each letter. The terms below are all like terms:
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,
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.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:
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.
Each is an xy2 term, even though they have different coefficients.
Each is an (x + 1) term, even though they have different coefficients.
All number terms are also like terms.
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:
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.
...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.
...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.
In this example, a is a constant, x and y are variables.