Simplify The Following Expression by Combining Like Terms Calculator
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Reviewed by Calculator Editorial Team
Simplifying algebraic expressions by combining like terms is a fundamental skill in algebra. This calculator helps you quickly simplify expressions and understand the process step-by-step.
What Are Like Terms?
Like terms are terms in an algebraic expression that have the same variable raised to the same power. For example, in the expression 3x + 5x² + 2x, the terms 3x and 2x are like terms because they both have the variable x raised to the first power.
Key Point: Like terms must have identical variable parts. The coefficients can be different.
How to Combine Like Terms
To combine like terms:
- Identify all terms that have the same variable raised to the same power.
- Add or subtract the coefficients of these terms.
- Keep the variable part unchanged.
Formula: If you have terms a·xⁿ + b·xⁿ, the simplified form is (a + b)·xⁿ.
Examples
Let's look at a few examples to see how combining like terms works:
Example 1
Expression: 4y + 7y - 2y
Solution: Combine the coefficients: (4 + 7 - 2)y = 9y
Example 2
Expression: 3x² + 5x - 2x² + 4x
Solution: Combine like terms: (3x² - 2x²) + (5x + 4x) = x² + 9x
Common Mistakes
When combining like terms, it's easy to make these mistakes:
- Adding terms with different variables (e.g., 3x + 2y)
- Adding terms with different exponents (e.g., 4x + 5x²)
- Forgetting to combine all like terms in the expression
When to Use This Calculator
This calculator is useful when you need to:
- Simplify algebraic expressions for homework or exams
- Prepare for standardized tests like the SAT or ACT
- Check your work when doing algebra problems
- Learn the process of combining like terms
Frequently Asked Questions
What is the difference between like terms and unlike terms?
Like terms have the same variable and exponent, while unlike terms have different variables or exponents.
Can I combine terms with different coefficients?
Yes, you can combine terms with different coefficients as long as they have the same variable and exponent.
What if there are no like terms in an expression?
The expression is already simplified, and no further combining is needed.