expands out products and positive integer powers in expr.
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Basic Examples (3)
Basic Uses (9)
Expand expressions involving arbitrary functions:
Expand does not go into subexpressions; ExpandAll does:
Expand applies to the numerator only:
ExpandAll applies to both the numerator and denominator:
Verify the equality of an expanded polynomial and its factored form:
Expand accepts polynomials with real or complex coefficients as inputs:
Expand threads over lists:
Expand threads over equations and inequalities:
Calculate the characteristic polynomial of a diagonal matrix:
The characteristic polynomial is the determinant of the following matrix:
Expand the product of diagonal elements to get the characteristic polynomial:
This can be directly computed using the CharacteristicPolynomial function:
Cyclotomic polynomials are monic, with integer coefficients, and are irreducible over the rational numbers.
The 16th cyclotomic polynomial is given below:
Use Expand to show that it has integer coefficients:
These polynomials can be directly computed using the Cyclotomic function:
Expand can be used to verify that two expressions are equal:
Properties & Relations (3)
Many functions give results in unexpanded form:
Factor is essentially the inverse of Expand:
When no powers are involved, Distribute gives the same results as Expand:
Direct application of the distributive law often generates far more terms than are needed:
Wolfram Research (1988), Expand, Wolfram Language function, https://reference.wolfram.com/language/ref/Expand.html (updated 2007).
Wolfram Language. 1988. "Expand." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/Expand.html.
Wolfram Language. (1988). Expand. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Expand.html