Algebraic Expression Simplifier

Enter any algebraic expression into the Algebraic Expression Simplifier and get the simplified form back. Type your expression using standard notation — for example, 2x + 3x - 5 + 7 or (x^2 - 4)/(x - 2) — and the tool will combine like terms, reduce coefficients, and display the result. Supports polynomials, basic rational expressions, and multi-variable terms.

Use ^ for exponents. Supported: polynomials, like-term combinations, basic simplification.

The main variable in your expression (used for ordering terms).

Results

Simplified Expression

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Number of Terms (Original)

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Number of Terms (Simplified)

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Terms Reduced

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Degree of Expression

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Coefficient Breakdown by Power

Results Table

Frequently Asked Questions

What does it mean to simplify an algebraic expression?

Simplifying an algebraic expression means rewriting it in a more compact form without changing its value. The most common method is combining like terms — terms that share the same variable and exponent are added or subtracted together. For example, 3x + 2x simplifies to 5x.

Why should I simplify expressions?

Simplified expressions are easier to evaluate, solve, and understand. A cleaner expression reduces the chance of arithmetic errors in further calculations, makes patterns more visible, and is often required before solving equations or graphing functions.

What are like terms in algebra?

Like terms are terms in an expression that have the same variable(s) raised to the same power. For example, 4x² and -2x² are like terms because they both contain x². Constants like 5 and -3 are also like terms. Unlike terms — such as 3x and 3x² — cannot be directly combined.

What notation should I use when entering an expression?

Use ^ for exponents (e.g. x^2 for x²), * for multiplication (e.g. 3*x or just 3x), and standard + and - for addition and subtraction. Parentheses are supported for grouping. Example inputs: 2x^2 + 3x - x^2 + 5 or (x+3)(x-3).

Can this tool simplify expressions with multiple variables?

Yes — expressions involving multiple variables such as 2xy + 3xy - x or 4a²b + a²b are supported. Like terms are grouped by matching both the variable combination and the exponents of each variable.

What is the degree of a polynomial expression?

The degree of a polynomial is the highest exponent of the variable in the simplified expression. For example, 3x² + 2x - 1 has degree 2 (a quadratic), and 5x³ - x has degree 3 (a cubic). The degree is useful for understanding the behavior and graph shape of the expression.

What is the difference between simplifying and factoring?

Simplifying typically means combining like terms to produce the most compact equivalent form. Factoring means rewriting an expression as a product of simpler expressions — for example, x² - 4 factors to (x+2)(x-2). Both are valid algebraic operations but serve different purposes.

Does simplifying an expression change its value?

No — simplification always produces an equivalent expression. For any value of the variable(s), the original and simplified expressions return the same result. Simplification only changes the form, not the mathematical meaning or value of the expression.

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