Use the Simplify > Expand command or press Ctrl+E to expand the currently highlighted expression or subexpression with respect to some or all of its variables.  (Note that the Expansion FunctionsExpansion_Functions can also be used to expand an expression.)  If only a subexpression is highlighted, the result is a copy of the whole expression with just the subexpression expanded.  This command displays a dialog box with fields for specifying the denominator factoring type and the expansion variables.


If a polynomial is expanded, the polynomial expansion is returned (see Expanding PolynomialsExpanding_Polynomials).  If a rational function is expanded, the partial fraction expansion is returned (see Expanding Rational FunctionsExpanding_Rational_Functions).


The Denominator Factoring Type field allows you to specify the amount of factoring to use on the denominator of rational functions:

•        Trivial content to factor out the trivial content of the terms of the denominator.

•        Squarefree polynomial to factor the denominator to factors that are free of perfect powers.

•        Rational polynomial to factor the denominator as much as possible without introducing fractional powers or complex numbers.

•        Radical polynomial to factor the denominator as much as possible without introducing complex factors.


The Expansion Variables field displays a list of all the variables in the highlighted expression or subexpression, and allows you to select the desired expansion variables.  Click on the desired primary expansion variable, then click on the secondary expansion variable, etc.  These expansion variables temporarily override the ordering specified by the variable order listed on the Output tab of the Options > Mode Settings command3L4YH.


Depending on the expression, the type of expansion, and the expansion variables, it may take a long time to expand an expression.  Click on the Calculation Progress dialog box's Abort button or press the Esc key to abort an Simplify > Expand command that is taking too long (for details, see the Simplify > Basic commandBQ.NIL).  You can then try expanding only portions of the expression or expanding with respect to a different variable.  These actions may drastically reduce the computing time and improve the comprehensibility of a result.


Note that the Simplify > Expand command and the Simplify > Basic commandBQ.NIL both transform an expression into a sufficiently simple formSufficiently_simple_form.  However, the Simplify > Basic command is often much faster and usually yields an expression more similar to the original expression.


Note that the Simplify > Expand command does not expand expressions involving the elementary functions.  To expand such expressions see Exponential FunctionsExponential_Functions, Logarithmic FunctionsLogarithmic_Functions, and Trigonometric FunctionsTrigonometric_Functions.


Other Simplify commandsSimplify_commands 

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