What are like terms in an expression examples?

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

For example: 3x and 10x are like terms (both have the variable x, raised to the 1st power). 14a2 and ba2 are also like terms (both have the variable a, raised to the 2nd power).

This page will show you how to identify and combine like terms.

Before discussing like and unlike terms, let’s take a quick review of an algebraic expression. In mathematics, an algebraic expression is a mathematical sentence made up of variables and constants, and operators such as addition and subtraction.

A variable in the expression is a term whose value is unknown, whereas a constant term has a definite value. The numerical number that accompanies a variable is called a coefficient. Examples of algebraic expressions are 3x + 4y -7, 4x – 10, 2x2 − 3xy + 5 etc.

In this article, we will learn the meaning of like terms and how to combine them.

What does Combine Like Terms mean?

Terms in an algebraic expression are normally separated by addition or subtraction.

For instance, a monomial expression has only one term. For example, 3x, 5y, 4x, etc. Similarly, a binomial expression contains two terms, for instance, 3x + y, 2x + 7, x + y etc. A trinomial contains three terms, whereas polynomials of higher degrees contain many terms.

Like terms in Algebra are terms that contain identical variables and exponents, regardless of their coefficients. Like terms are combined in algebraic expression so that the result of the expression can be calculated with ease.

For example, 7xy + 6y + 6xy is an algebraic equation whose terms are 7xy and 6xy. Therefore, this expression can be simplified by combining like terms as 7xy + 6xy + 6y = 13xy + y. You can note that, when combining like terms, we only add the coefficients of the terms.

On the other hand, unlike terms are terms that do not have identical variables and exponents.

For example, an expression 4x + 9y contains terms because variables x and y are different and are not raised to the same power.

How to Combine the Like Terms?

Let’s understand this concept with the help of a few examples.

Example 1

Consider the expression: 4x + 3y.

This expression cannot be simplified because x and y are two different variables;

Example 2

To simplify an expression 4x² + 3x + 4y + 8x + 10x²;

Solution

Collect and add the like terms which gives; 10x² + 4x²+ 8x + 3x + 4y => 14x² + 11x + 4y.

From this example, we can conclude as the terms also have the same variables raised to the same exponent.

Example 3

Simplify 2xy + 4x² + 5yx +5y² +16x².

Solution

In this example, the terms 2xy and 5yx, as well as 4x² and 16 x² have identical variables. 2xy and 5yx are identical because of the commutative property of multiplication. Therefore, 2xy + 5yx = 7xy and 4x² +16x² = 20 x².

Even without knowing what a variable is, we can sometimes make expressions with variables look simpler. This is done by simplifying our expression.

Here is a vocabulary word that will help you understand the lesson better:

• Coefficient = the number being multiplied to a variable (in 2n, 2 is the coefficient)
• Reduce = combine or simplify by doing whatever operations we can
• Term = a part of an expression separated from the rest by addition (in 3a + 6b, 3a is one term and 6b is another term)
• Like Terms = any terms in an expression where the variables are the same (3a and 4a, \(2{\text{b}}^{2}\) and \(5{\text{b}}^{2}\), note that \(2{\text{b}}^{2}\) and 3b are not like terms)

Video Source (09:10 mins) | Transcript

Remember to follow the order of operations. Sometimes this means to use the distributive property to solve what’s in the parentheses.

When we see two different letters, we can easily know that we don’t have like terms, but can we add \(3{\text{a}} + 4{\text{a}}^{2}\) ? Let’s say \({\text{a}}=3\), then \({\text{a}}^{2}=9\). Because these are different numbers the answer is no, we cannot add \(3{\text{a}}+4{\text{a}}^{2}\). Any time we have different letters as our variables, or the same letter with different powers, we do not have like terms.

Additional Resources

• Khan Academy: Intro to Combining Like Terms (04:32 mins, Transcript)
• Khan Academy: Simplifying Expressions (04:06 mins, Transcript)
• Khan Academy: Combining Like Terms - Challenge Problem (04:38 mins, Transcript)

Practice Problems

Simplify the following expressions:

1. 7w − 2w


2. 5s − 7 − 3s + 11


3. 5a − 2b − 6 + 3a + 6b


4. \(2{\text{v}}^{2}+6+3{\text{v}}{-}3{\text{v}}^{2}\)


5. \( 2(3-2{\text{t}}) + 5 ({\text{t}} + 3) \)


6. \( ( 4 {\text{x}} + 3 {\text{y}} - 2{\text{z}} ) - 2 ( {\text{x}} + 3 {\text{z}}) \)

Solutions

1. 5w (Written Solution)

   The terms 7w and 2w have the same variable, w. They are like terms.

   \(7{\text{w}} {-} 2{\text{w}}\)

   The problem seems to have had a w distributed into each term. Using the knowledge of the Distributive Property, undo the distribution above, this is called factoring. Place the numbers 7−2 inside parentheses and the variable, w, outside the parentheses. Like this \({\text{w}} (7 - 2) \).

   \({\text{w}} (7 - 2)\)

   Subtract \(7-2\).

   \(\text w({\color{Red} 7-2})\)

   Replace the subtraction of 7−2 with the answer 5.

   \(\text w({\color{Red} 5})\)

   To show your solution in standard mathematical form, remove the parentheses and move the variable to the right of the number. The simplified expression is 5w.

   \(5\)\({\text{w}}\)



2. 2s + 4 (Written Solution)

   One way to simplify this problem is to move the like terms, and their signs, near each other.

   5s − 7 − 3s + 11

   Move the -7 to the end, next to the 11. This allows the two sets of like terms to be placed near each other.

   5s − 3s + 11 − 7

   Now find the difference between 5s and 3s.

   5s − 3s + 11 − 7

   Replace 5s − 3s with the difference of 2s.

   2s + 11 − 7

   Now, find the difference between 11 and 7

   2s + 11 − 7

   Replace \(11-7\) with the difference of 4.

   2s + 4

   This problem simplifies to 2s + 4



3. 8a + 4b − 6 (Solution Video | Transcript)


4. \(-{\text{v}}^{2}+3{\text{v}}+6\) (Written Solution)

   Start by combining the like terms. First find the difference between \(2{\text{v}}^{2}\) and \(-3{\text{v}}^{2}\).

   \(2{\text{v}}^{2}+6+3{\text{v}}{-}3{\text{v}}^{2}\)

   The difference between \(2{\text{v}}^{2}\) and \(-3{\text{v}}^{2}\) is \(-1{\text{v}}^{2}\). Remove \(2{\text{v}}^{2}\) and \(-3{\text{v}}^{2}\) and replace with \(-{\text{v}}^{2}\).

   \(-{\text{v}}^{2}+6+3{\text{v}}\)

   Move the terms to standard mathematical form. Move the \(+3{\text{v}}\) in between \({\text{v}}^{2}\) and \(+6\).

   What are examples of like terms?

   Examples: 7x and 2x are like terms because they are both "x". 3x2 and −2x2 are like terms because they are both "x2". But 7x and 7x2 are NOT like terms (the exponents are different), they are unlike terms.

   Are 5x and 4xy like terms?

   Now the answer to the above question is NO, 5x and 4xy are not like terms as 5x and 4xy both have different variables with different coefficient of x and y.

   Are 2x and 3x like terms?

   Summary. Like terms are terms that have exactly the same variable and power in them—whether that's x, x3, y, or even no variable! So, for example, 2x and 3x would be like terms since they both have the variable x and they're both to the first power.