Combine Like Terms Calculator

Author: Henrick Yau
- May 21, 2025
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Calculators

Simplify algebraic expressions by combining like terms. Enter an expression with variables and constants to see the step-by-step solution.

Enter Algebraic Expression

Use x, y, z as variables. Include spaces around operators (+ and -) for better parsing.

Examples to Try

How to Combine Like Terms

Combining like terms is a fundamental algebraic technique used to simplify expressions. Like terms have the same variables raised to the same powers.

Rules for Combining Like Terms
  1. Identify terms with identical variable parts (e.g., all terms with x, all terms with x²)
  2. Add or subtract the coefficients of like terms
  3. Keep the variable part unchanged
  4. Combine all constant terms (numbers without variables)
Examples
  • 3x + 5x = 8x (3 and 5 are coefficients of like term x)
  • 2y² - 7y² = -5y² (2 and -7 are coefficients of like term y²)
  • 4xy + 2xy = 6xy (4 and 2 are coefficients of like term xy)
  • 5 + x - 2 = x + 3 (5 and -2 are constants that can be combined)
Terms That Are Not Like Terms
  • x and y (different variables)
  • x and x² (same variable but different exponents)
  • xy and x²y (different powers of variables)
  • 2x and 2 (variable term vs. constant term)

Note: This calculator handles polynomial expressions with variables. For more complex expressions involving fractions, trigonometric functions, or other special functions, consider using a more advanced algebraic calculator.

Simplifying Algebraic Expressions Made Easy

The Combine Like Terms Calculator is a user-friendly math solver tool that simplifies algebraic expressions by grouping and merging similar terms. This helps students, educators, and anyone learning algebra to quickly understand and simplify mathematical expressions without needing manual calculations.

It is especially useful for middle school, high school, and early college-level learners studying linear equations, polynomial expressions, and basic algebra rules.

Formula for Combining Like Terms

ax + bx = (a + b)x

mxy + nxy = (m + n)xy

c + d = (c + d) (for constants)

Enter an Expression and Combine Like Terms

Follow these simple steps to simplify an algebraic expression:

  • Enter your expression in the input field (e.g., 3x + 2y - 5x + 7 + 4y - 2).
  • Click on Combine Like Terms.
  • Optionally, check or uncheck Show step-by-step solution to display the breakdown.
  • Use the example buttons for instant demos and inspiration.

The tool provides a simplified result, a visual explanation of how terms are grouped, and a step-by-step guide for better understanding.

Who Benefits from This Algebra Tool

This calculator is helpful for:

  • Students learning how to simplify algebraic expressions
  • Teachers looking to demonstrate algebra steps clearly
  • Anyone preparing for standardized tests like the SAT, ACT, or GRE
  • Learners practicing for other tools such as a scientific calculator, matrix solver, or percent error calculator

Why Combining Like Terms Is Important

Simplifying expressions makes solving equations faster and less prone to error. It also lays the groundwork for solving more advanced problems in algebra, trigonometry, and calculus. Understanding how to combine like terms improves skills that are essential in using tools such as:

  • Fraction Calculator – to simplify and combine fractional expressions
  • Exponent Calculator – for simplifying powers after combining terms
  • Percent Error Calculator – for analyzing how simplified expressions affect error percentage calculation
  • Scientific Calculator – when evaluating more complex algebraic or trigonometric expressions

Common Questions About Combining Like Terms

What are “like terms” in algebra?

Like terms are terms that have the exact same variable part (including exponents). For example, 3x and -5x are like terms, but x and x² are not.

What does this calculator do with constants?

It adds or subtracts constant numbers (like 5 or -2) the same way it handles variables.

Can it handle powers and multiple variables?

Yes. Terms like 2xy and -3xy are combined, and it understands powers such as x² or a². However, x and x² are treated as separate groups.

Does it work for equations with equal signs?

No, this calculator is designed for expressions, not full equations. It won't solve for unknowns like a quadratic formula calculator or system of equations solver.

Is this tool a replacement for a scientific calculator?

Not exactly. While this tool simplifies expressions, a scientific calculator can handle a broader range of functions like trigonometry and logarithms.

Save Time and Learn Algebra Step by Step

Using this calculator saves time and reduces errors. It provides:

  • Instant simplification of algebraic expressions
  • Clear, step-by-step explanations that reinforce learning
  • Visual grouping of like terms to support deeper understanding
  • A foundation for using more advanced tools like a matrix computation solver or logarithm calculator

It’s especially beneficial for those wanting to learn how to simplify algebra before moving on to more advanced math problem solvers or working with a full scientific calculator.

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