## Algebraic transformations

Mathematica can perform many of the most common transformations of algebraic expressions.

Algebraic operators
Mathematicaresultexample
Expand[algebraic product]expands out products and powersExpand[(x^2+1)(x-1)^2]
Factor[algebraic sum]factors sums into products and powersFactor[x^2-3x+2]
Together[sum of fractions]gives the sum of algebraic fractionsTogether[x+1/x+1/(x+1)]
Simplify[algebraic fraction]simplifies an algebraic fractionSimplify[(x^2+2x+1)/(x^2-1)]
Apart[algebraic fraction]write an algebraic fraction with minimum denominatorApart[(x^2+1)/(x-1)]
TrigExpand[trigonometric expression]expands expressions on circular or hyperbolic functionsTrigExpand[Cos[x+y]]
TrigFactor[trigonometric expression]factors expressions on circular or hyperbolic functionsTrigFactor[Sin[x]Cos[y]+Sin[y]Cos[x]]

Example: Expand

Other examples.

WolframAlpha: Factor

WolframAlpha: Together

WolframAlpha: Simplify

WolframAlpha: Apart

WolframAlpha: TrigExpand

WolframAlpha: TrigFactor