The Wolfram Language handles formulas of all types, from polynomials with millions of terms to complex combinations of higher mathematical functions. It provides powerful general transformation and simplification functions that automatically call on thousands of rules and algorithms—many original to Wolfram Research.

Simplify — simplify, perhaps with assumptions about variables

FullSimplify — apply full simplification procedures

FunctionExpand — expand in terms of more elementary functions

Expand — expand out algebraic expressions

Factor — factor algebraic expressions

Reduce — reduce out equations and inequalities

Series — find a series approximation

Extracting Parts of Formulas

Coefficient   ▪ Exponent   ▪ Part   ▪ Numerator   ▪ Denominator

Formula Rearrangement

Collect   ▪ Together   ▪ Apart   ▪ Cancel

Equation Transformations

AddSides   ▪ SubtractSides   ▪ MultiplySides   ▪ DivideSides   ▪ ApplySides

Algebraic Transformations »

PowerExpand   ▪ ComplexExpand   ▪ TrigExpand   ▪ RootReduce   ▪ ComplexityFunction   ▪ ...

Formula Testing

Equal (== )  ▪ Element   ▪ PossibleZeroQ

Assumptions & Domains »

Refine   ▪ Assuming   ▪ ForAll   ▪ Integers   ▪ Reals   ▪ ...

TraditionalForm — display a formula in traditional math notation

Related Tech Notes

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• Simplification
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• Simplifying Algebraic Expressions
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• Simplifying with Assumptions
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• Picking Out Pieces of Algebraic Expressions
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• Putting Expressions into Different Forms
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• Structural Operations on Rational Expressions

Related Guides

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• Polynomial Algebra
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• Rational Functions
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• Pattern Matching
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• Inequalities

Related Links

• Demonstrations related to Formula Manipulation (Wolfram Demonstrations Project)
• Wolfram Community: Mathematics