Mathematica simplify with substitution

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The simplify command finds the simplest form of an equation.
Simplify[expr,assum] does simplification using assumptions.
Expand[expr,patt] leaves unexpanded any parts of expr that are free of the pattern patt.

ExpandAll[expr] expands out all products and integer powers in ant part of exps.
ExpandAll[expr,patt] avoids expanding parts of expr that do not contain terms matching the pattern patt.

One of Mathematica’s most useful features for new users is algebraic manipulation.

Fullsimplify mathematica

The program enables the user to avoid tedious exercises in simplification, expansion, and manipulation of algebraic expressions. For example, rather than spending odious amounts of time using the distributive property, Mathematica allows the user to quickly discover that \( (x-1)(x-7)(x+2)(x-4) = x^4 -10\,x^3 + 15\, x^2 + 50\, x -56.

\)

D[Integrate[1/(x^3 + 1), x], x] (* integrate the expression *)

Out[1]= 1/(3 (1 + x)) - (-1 + 2 x)/(6 (1 - x + x^

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