Like and Unlike Terms in Algebra – Easy Explanation with Examples
Like and unlike terms are one of the most important basic concepts in algebra. Understanding them helps students simplify expressions, solve equations, and avoid common mistakes. In this post, we will explain like and unlike terms in a very easy way, with clear examples suitable for beginners.
What Are Terms in Algebra?
In algebra, a term is a part of an expression that can include:
- A number (called a coefficient)
- A variable (such as x, y, or z)
- An exponent (power of a variable)
Examples of algebraic terms:
- 3x
- 5y2
- −7
- 4ab
What Are Like Terms?
Like terms are terms that have:
- The same variable(s)
- The same exponent(s)
The numbers in front (coefficients) can be different, but the variable part must be exactly the same.
Examples of Like Terms
- 3x and 7x
- 5y2 and −2y2
- 4ab and −9ab
- 8 and −3 (constants are also like terms)
Why are they called like terms?
Because they represent the same type of quantity and can be combined.
What Are Unlike Terms?
Unlike terms are terms that do not have the same variable part.
They may differ in:
- Variables (x and y)
- Exponents (x and x2)
- Both variables and exponents
Examples of Unlike Terms
- 3x and 3y
- 5x and 5x2
- 2a and 2ab
- x and y2
Important: Unlike terms cannot be combined.
Like vs Unlike Terms (Quick Comparison)
| Like Terms | Unlike Terms |
|---|---|
| Same variables | Different variables |
| Same exponents | Different exponents |
| Can be combined | Cannot be combined |
Examples Explained Step by Step
Example 1
3x + 5x
Both terms have the same variable x.
Answer: 8x
Example 2
4y + 2y2
The variables are the same, but the exponents are different.
These are unlike terms and cannot be combined.
Example 3
7a − 3b
Different variables (a and b).
These are unlike terms.
Why Are Like and Unlike Terms Important?
Understanding like and unlike terms helps students to:
- Simplify algebraic expressions
- Add and subtract polynomials correctly
- Avoid common algebra mistakes
- Prepare for advanced topics like factorization
Practice Questions
Identify whether the following pairs are like or unlike terms:
- 6x and −2x
- 3y and 3y2
- 5a and 5b
- 9 and −4
Conclusion
Like and unlike terms form the foundation of algebra. Once students understand how to identify them, simplifying expressions and solving equations becomes much easier. Always check the variables and exponents before combining terms.
Next Step: Learn how to use like terms in simplifying algebraic expressions.
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