Collecting Like Terms: Definition, Examples, and Questions
Collecting like terms is an important step in simplifying algebraic expressions. In this lesson, you'll learn what like terms are, how to collect like terms, and you'll see some examples to help you practice.
What are Like Terms?
Like terms are terms that have the same variable or combination of variables raised to the same power. Only like terms can be added or subtracted in algebraic expressions.
For example:
- 2x and 5x are like terms because both include x to the same power.
- 3a and 7b are not like terms because they have different variables.
- 4x² and 3x² are like terms because both include x².
How to Collect Like Terms
- Identify the like terms in the expression.
- Group the like terms together (including their signs).
- Add or subtract the coefficients of the like terms.
Examples of Collecting Like Terms
Example 1:
Simplify 3c + 8c - 2c
Solution:
- All terms are like terms (they all contain c).
- Add or subtract the coefficients: 3c + 8c - 2c = 9c.
Answer: 9c
Example 2:
Simplify 5f + 8 + 13f + 3
Solution:
- 5f and 13f are like terms; 8 and 3 are constants (like terms).
- Add the like terms: 5f + 13f = 18f, and 8 + 3 = 11.
Answer: 18f + 11
Example 3:
Simplify 3a + 2b + 13 + 7a + 3b + 4
Solution:
- Group the like terms: 3a + 7a, 2b + 3b, and 13 + 4 are like terms.
- Add: 3a + 7a = 10a, 2b + 3b = 5b, and 13 + 4 = 17.
Answer: 10a + 5b + 17
Collecting Like Terms Practice Questions
Question 1
Simplify: \( 3a + 5a - 2a \)
Collecting Like Terms with Powers
Example 4:
Simplify 2x + 3x² + 5x
Solution:
- 2x and 5x are like terms; 3x² is not like them because of the exponent.
- Add the like terms: 2x + 5x = 7x.
Answer: 7x + 3x²
Example 5:
Simplify x² - 5x + 4x² - 4 + 7x
Solution:
- x² and 4x² are like terms; -5x and 7x are like terms; -4 is a constant.
- Add the like terms: x² + 4x² = 5x² and -5x + 7x = 2x.
Answer: 5x² + 2x - 4
Example 6:
Simplify ab² - 3a²b + 4ab² - 4a²b² + 7a²b
Solution:
- ab² and 4ab² are like terms; -3a²b and 7a²b are like terms; -4a²b² has no like terms.
- Add the like terms: ab² + 4ab² = 5ab² and -3a²b + 7a²b = 4a²b.
Answer: 5ab² + 4a²b - 4a²b²
Collecting Like Terms Practice Questions (Including Powers)
Question 1
Simplify: \( 4x^2 + 3x - x^2 + 2x \)