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ExpandAll[expr]

expands out all products and integer powers in any part of expr.

ExpandAll[expr,patt]

avoids expanding parts of expr that do not contain terms matching the pattern patt.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Modulus  
Trig  
Applications  
See Also
Tech Notes
Related Guides
History
Cite this Page

ExpandAll

ExpandAll[expr]

expands out all products and integer powers in any part of expr.

ExpandAll[expr,patt]

avoids expanding parts of expr that do not contain terms matching the pattern patt.

Details and Options

  • ExpandAll[expr] effectively maps Expand and ExpandDenominator onto every part of expr.
  • ExpandAll automatically threads over lists in expr, as well as equations, inequalities and logic functions.
  • ExpandAll takes the following options:
  • Modulus 0modulus to assume for integers
    Trig Falsewhether to do trigonometric as well as algebraic transformations

Examples

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Basic Examples  (1)

Expand polynomials anywhere inside an expression:

Wolfram Language code: ExpandAll[1 / (1 + x) ^ 3 + Sin[(1 + x) ^ 3]]
Wolfram Language code: Expand[1 / (1 + x) ^ 3 + Sin[(1 + x) ^ 3]]

Scope  (6)

Expand the numerator and the denominator of a rational expression:

Wolfram Language code: ExpandAll[(x + z) ^ 2 / (x + y) ^ 2]

Expand the exponent:

Wolfram Language code: ExpandAll[E ^ (I a (t - b))]

ExpandAll goes into heads:

Wolfram Language code: ExpandAll[((1 + a) (1 + b))[x]]

Expand only subexpressions involving :

Wolfram Language code: ExpandAll[(f[(x + y) ^ 2] + g[(y + z) ^ 2]) ^ 2, x]

Expand the expression over the integers modulo :

Wolfram Language code: ExpandAll[6z / (2x + 3y) ^ 6, Modulus -> 4]

Expand the expression using expansion formulas for trigonometric functions:

Wolfram Language code: ExpandAll[(a - b) ^ 2 / (Sin[2x] + 1), Trig -> True]

Options  (2)

Modulus  (1)

Expand a rational function over the integers modulo 3:

Wolfram Language code: ExpandAll[z / (x + y) ^ 3, Modulus -> 3]

Trig  (1)

Expand numerator and denominator using expansion formulas for trigonometric functions:

Wolfram Language code: ExpandAll[(a - b) / (Sin[x + y] + 1), Trig -> True]

Applications  (1)

Verify that two expressions are equal:

Wolfram Language code: expr1 = Sin[(x + 1) ^ 2] + 1 / (x ^ 2 - 1)
Wolfram Language code: expr2 = Sin[x ^ 2 + 2x + 1] + 1 / ((x - 1)(x + 1))

Use ExpandAll to show that the expressions are equal:

Wolfram Language code: ExpandAll[expr1] == ExpandAll[expr2]

Expand is not sufficient to verify the equality:

Wolfram Language code: Expand[expr1] == Expand[expr2]
Wolfram Research (1988), ExpandAll, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpandAll.html (updated 2007).

Text

Wolfram Research (1988), ExpandAll, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpandAll.html (updated 2007).

CMS

Wolfram Language. 1988. "ExpandAll." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/ExpandAll.html.

APA

Wolfram Language. (1988). ExpandAll. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ExpandAll.html

BibTeX

@misc{reference.wolfram_2026_expandall, author="Wolfram Research", title="{ExpandAll}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ExpandAll.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_expandall, organization={Wolfram Research}, title={ExpandAll}, year={2007}, url={https://reference.wolfram.com/language/ref/ExpandAll.html}, note=[Accessed: 13-June-2026]}