Being able to collect like terms is an important skill in simplifying expressions in mathematics. You’ll need to learn this not only to simplify expressions but to solve equations which are not already simplified.
In this lesson you’ll learn what ‘like terms’ means and what it means to ‘collect like terms’ in algebra.
What does ‘collecting like terms’ mean?
Collecting like terms means to identify any repeated variables in algebraic expressions and to simplify them by adding or subtracting.
What is a ‘like term’?
A like term is a variable or product of variables which appears more than once in an algebraic expression.
For example 3a, 5a, and -6a are all like terms because they include the same variable a.
3a and 5b are not like terms because they are different variables.
What is an example of collecting like terms?
Example 1: 8a – 5a = 3a
Here the variable a appears in both terms of the expression so we can simplify by subtracting 5a from 8a.
Example 2: 2a + 3b + 5a + 6b = 7a + 9b
Here both variables a and b appear twice so we can simplify: 2a + 5a = 7a and 3b + 6b = 9b.
How to collect like terms
- Identify the like terms.
- Group the like terms together (including their positive or negative signs).
- Simplify the like terms by adding or subtracting.
Read some examples to fully understand the step-by-step process.
Collecting Like Terms Examples
Collecting Like Terms: One Variable Only
Example 1
Simplify 3c + 8c – 2c
Step 1: Identify like terms
All three terms terms are like terms as they have the same variable c.
Step 2: Group like terms
They are already grouped together.
Step 3: Add/subtract like terms
3c + 8c – 2c = 9c
Answer: 9c
Example 2
Simplify 5f + 8 + 13f + 3
Step 1: Identify like terms
5f and +13f are like terms as they both include f
8 and 3 are constants (numbers)
Step 2: Group like terms
5f + 13f + 8 + 3
Step 3: Add/subtract like terms
5f + 13f + 8 + 3 = 18f + 11
Answer: 18f + 11
Collecting Like Terms: Multiple Variables and Constants
Example 3
Simplify 3a + 2b + 13 + 7a + 3b + 4
Step 1: Identify like terms
3a and +7a are like terms as they both include a
+2b and +3b are like terms as they both include b
13 and 4 are constants
Step 2: Group like terms
3a + 7a + 2b + 3b + 13 + 4
Step 3: Add/subtract like terms
3a + 7a + 2b + 3b + 13 + 4 = 10a + 5b + 17
Answer: 10a + 5b + 17
Collecting Like Terms With Negatives
When collecting like terms with negative numbers, remember to include the positive or negative sign before the number. For example in 9x – 6x + 2y – 3y, the negative signs should stay in front of -6x and -3y when regrouping.
Example 4
Simplify 9x – 6x + 2y – 3y
Step 1: Identify like terms
9x and -6x are like terms as they both include x
+2y and –3y are like terms as they both include y
Step 2: Group like terms
9x – 6x + 2y – 3y
Don’t forget to include the positive or negative sign which comes before the term.
Step 3: Add/subtract like terms
9x – 6x + 2y – 3y = 3x – y
Note: We write -y instead of -1y
Answer: 3x – y
Collecting Like Terms With Powers
When collecting like terms with powers, different powers are treated as different terms.
For example in 2x + 3x2 + 5x, 2x and 5x are like terms but 3x2 is not as it has a different power of x.
When terms include more than one variable and have different powers, the variables and powers must be the same to be considered like terms.
For example in 3x2y + 5xy2 + 6xy2 + 2x2y, only the first and last terms 3x2y and 2x2y are like terms because they both have the same powers of x and y.
The terms 5xy2 and 6xy2 have different powers for x and y so they cannot be added together.
Here are some more examples to clarify.
Example 5
x2 – 5x + 4x2 – 4 + 7x
Step 1: Identify like terms
x2 and 4x2 are like terms as they both include x2
–5x and +7x are like terms as they both include x
-4 is the only constant
Step 2: Group like terms
x2 + 4x2 – 5x + 7x – 4
Don’t forget to include the positive or negative sign which comes before the term.
Step 3: Add/subtract like terms
x2 + 4x2 – 5x + 7x – 4 = 5x2 + 2x – 4
Answer: 5x2 + 2x – 4
Example 6
ab2 – 3a2b + 4ab2 – 4a2b2 + 7a2b
Step 1: Identify like terms
ab2 and 4ab2 are like terms
–3a2b and +7a2b are like terms
–4a2b2 has no like terms
Step 2: Group like terms
ab2 + 4ab2 – 3a2b + 7a2b – 4a2b2
Step 3: Add/subtract like terms
ab2 + 4ab2 – 3a2b + 7a2b + 4a2b2 = 5ab2 + 4a2b – 4a2b2
Answer: 5ab2 + 4a2b – 4a2b2
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