Simplify Calculator
Simplify any algebraic expression instantly — polynomials, fractions, exponents, and more. Get the fully reduced form with step-by-step solutions.
Examples: 3x + 2x - x , 2(x+3) + 4x , (x^2-4)/(x-2)
Simplification Examples
| Expression | Simplified | Rule Applied |
|---|---|---|
| 3x + 2x - x | 4x | Combine like terms |
| 2(x + 3) + 4x | 6x + 6 | Distribute and combine |
| x^2 + 5x + 6 | (x+2)(x+3) | Factor a trinomial |
| (x^2 - 4) / (x - 2) | x + 2 | Cancel common factors |
| 3x^2 - 3x^2 + 7 | 7 | Eliminate zero terms |
| (2x)^3 | 8x³ | Apply power rule |
How to Simplify Algebraic Expressions — Step-by-Step
Simplifying an algebraic expression means rewriting it in its most compact form without changing its value. Follow these steps in order:
- 1Remove parentheses — Use the distributive property: multiply the term outside by each term inside. Example: 2(x + 3) = 2x + 6
- 2Combine like terms — Add or subtract terms with identical variables and powers. Example: 3x + 5x = 8x, but 3x + 5x² cannot be combined.
- 3Apply exponent rules — Use power laws: x^a × x^b = x^(a+b), (x^a)^b = x^(ab), x^0 = 1.
- 4Cancel common factors — In fractions, factor numerator and denominator, then cancel matching terms. Example: (x²-4)/(x-2) = x+2.
- 5Write in standard form — Arrange terms from highest to lowest degree. Example: 3 + 5x + x² → x² + 5x + 3.
Types of Algebraic Simplification
Combining Like Terms
Add/subtract coefficients of identical variable terms. The foundation of all algebraic simplification.
Factoring
Rewrite as a product of simpler expressions. Useful for polynomials and rational expressions.
Rational Simplification
Cancel common factors in algebraic fractions to reduce them to lowest terms.
Exponent Simplification
Apply power laws to combine, expand, or reduce terms with exponents.
Radical Simplification
Reduce square roots by factoring out perfect squares. E.g., √12 = 2√3.
Trigonometric Simplification
Use identities like sin²x + cos²x = 1 to rewrite trig expressions more simply.
Frequently Asked Questions
How does the simplify calculator work?
Our simplify calculator analyzes your algebraic expression using mathematical rules — distributing, combining like terms, cancelling common factors, and applying exponent laws — to produce the most reduced form with a full step-by-step breakdown.
What types of expressions can I simplify?
You can simplify linear expressions (3x + 2x), polynomial expressions (x^2 + 5x + 6), rational expressions (fractions with variables), expressions with exponents, and expressions with square roots or radicals.
What is the difference between simplifying and solving?
Simplifying reduces an expression to its shortest equivalent form without finding a specific value. Solving an equation means finding the value(s) of the variable that make the equation true. Use our equation simplifier for solving equations.
Can I simplify expressions with multiple variables?
Yes. The calculator handles multi-variable expressions such as 3x + 2y - x + 5y, simplifying to 2x + 7y by combining like terms for each variable.
How do I enter exponents in the simplify calculator?
Use the caret symbol ^ to denote exponents. For example, x squared is entered as x^2, and x cubed as x^3. For square roots, enter sqrt(x) or x^(1/2).