Combine Like Terms Calculator

Author: Henrick Yau
- 9 October 2026
| |

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 xยฒ)
  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)
  • 2yยฒ - 7yยฒ = -5yยฒ (2 and -7 are coefficients of like term yยฒ)
  • 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 xยฒ (same variable but different exponents)
  • xy and xยฒy (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 with like terms

The Combine Like Terms Calculator is an easy-to-use maths tool that simplifies algebraic expressions by grouping and merging similar terms. It helps students, teachers, and anyone learning algebra to quickly understand and simplify mathematical expressions without needing to work them out by hand.

It is especially useful for learners in secondary school, sixth form, and early university who are 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)

Entering and simplifying an expression step by step

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, tick or untick 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 Is This Calculator For?

This calculator is helpful for:

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

Common questions about combining like terms

What are โ€œlike termsโ€ 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 xยฒ 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 xยฒ or aยฒ. However, x and xยฒ 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.

Benefits of using this algebra simplifier

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

Itโ€™s especially beneficial for those wanting to learn how to simplify algebra before moving on to more advanced maths problem solvers or working with a full scientific calculator.

Related maths tools and calculators

If you found this calculator useful, you may also like: