Combine Like Terms Calculator
Identify and combine like terms in algebraic expressions with detailed grouping
Enter an expression with multiple terms using variables and numbers
Understanding Like Terms
Like terms are terms in an algebraic expression that have identical variable parts, including the same variables raised to the same powers. Only the coefficients can differ.
What Makes Terms "Like"?
Two or more terms are considered like terms if they have:
- The exact same variables
- The same exponent on each variable
- Different coefficients (the numbers in front)
Examples of Like Terms
- ✓ 3x and 5x (same variable x)
- ✓ -2y² and 7y² (same variable y with same exponent 2)
- ✓ 4 and -9 (both are constants)
- ✗ 3x and 3y (different variables)
- ✗ 2x and 2x² (same variable, different exponents)
How to Combine Like Terms
- Identify all terms in the expression
- Group terms with identical variable parts
- Add or subtract the coefficients within each group
- Keep the variable part unchanged
- Write the simplified expression
Example
Combine like terms: 3x + 5x - 2y + 4y + 7 - 3
- x terms: 3x + 5x = 8x
- y terms: -2y + 4y = 2y
- Constants: 7 - 3 = 4
- Result: 8x + 2y + 4
Frequently Asked Questions
What are like terms?
Like terms are terms that have the same variables raised to the same powers. Only their coefficients (the numbers in front) can be different. For example, 3x and -5x are like terms.
Can I combine 3x and 3x²?
No, 3x and 3x² are not like terms because they have different exponents on the variable x. You can only combine terms with identical variable parts, including matching exponents.
Are constants like terms?
Yes! All constant terms (numbers without variables) are like terms and can be combined. For example, 5, -3, and 7 are all like terms and can be added together.
What happens to the variable when combining like terms?
The variable part stays exactly the same. You only add or subtract the coefficients. For example, 4x + 3x = 7x (not 7x²).
Can I combine terms with different variables?
No, terms with different variables are not like terms and cannot be combined. For example, 3x and 5y cannot be combined into a single term.
What about terms like 2xy and 3xy?
These are like terms! They have the exact same variable part (xy), so they can be combined: 2xy + 3xy = 5xy.
How do negative signs affect combining like terms?
Negative signs are part of the coefficient. When combining like terms, use the rules for adding and subtracting integers. For example, 5x - 3x = 2x, and -4y - 2y = -6y.
Why is combining like terms important?
Combining like terms simplifies expressions, making them easier to work with. It's an essential skill for solving equations, graphing functions, and performing other algebraic operations.
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