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ExpandNumerator[expr]

expands out products and powers that appear in the numerator of expr.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Modulus  
Trig  
Applications  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
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ExpandNumerator

ExpandNumerator[expr]

expands out products and powers that appear in the numerator of expr.

Details and Options

  • ExpandNumerator works on terms that have positive integer exponents.
  • ExpandNumerator applies only to the top level in expr.
  • ExpandNumerator automatically threads over lists, as well as equations, inequalities, and logic functions.
  • ExpandNumerator takes the following options:
  • Modulus 0modulus to assume for integers
    Trig Falsewhether to do trigonometric as well as algebraic transformations

Examples

open all close all

Basic Examples  (2)

Expand the numerator of a fraction:

Wolfram Language code: ExpandNumerator[(x - 1)(x - 2) / ((x - 3)(x - 4))]

Expand a numerator involving multiple variables:

Wolfram Language code: ExpandNumerator[(1 - x ^ 2 + y ^ 4 - z ^ 6) ^ 2 / ((x - 3)(y - 3))]

Scope  (7)

Expand the numerator of a rational function:

Wolfram Language code: ExpandNumerator[(x - y) ^ 2 / (u - v) ^ 2]

ExpandNumerator threads over sums:

Wolfram Language code: ExpandNumerator[(a + b) ^ 2 / x + (c + d)(c - d) / y]

ExpandNumerator threads over Boolean combinations of equations and inequalities:

Wolfram Language code: ExpandNumerator[x == (a + b) ^ 2 / c && y ≥ (a - b) ^ 2 / c]

ExpandNumerator does not separate the fraction; Expand does:

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

Expand numerator of a fraction involving arbitrary functions:

Wolfram Language code: ExpandNumerator[(Log[x] + 2 ^ x) ^ 3 / (Cos[x] + Sin[x]) ^ 2]

Expand the numerator using expansion formulas for trigonometric functions:

Wolfram Language code: ExpandNumerator[Sin[2x] / (x - 1) ^ 2, Trig -> True]

Expand the numerator over the integers modulo :

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

Options  (2)

Modulus  (1)

Expand the numerator over the integers modulo 3:

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

Trig  (1)

Expand the numerator using expansion formulas for trigonometric functions:

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

Applications  (1)

ExpandNumerator can be used to verify that two expressions are equal:

Wolfram Language code: ((1 - x^2)^2/1 + x^4) == ( (1 - x)^2 (1 + x)^2/1 + x^4)
Wolfram Language code: ExpandNumerator[%]

Properties & Relations  (5)

ExpandNumerator leaves the denominator unexpanded:

Wolfram Language code: ExpandNumerator[(a + b)(a - b) / ((c + d)(c - d))]

ExpandDenominator expands the denominator, leaving the numerator unexpanded:

Wolfram Language code: ExpandDenominator[(a + b)(a - b) / ((c + d)(c - d))]

Expand expands the numerator and expands the fraction into a sum of fractions:

Wolfram Language code: Expand[(a + b)(a - b) / ((c + d)(c - d))]

ExpandAll expands the numerator, the denominator, and the fraction:

Wolfram Language code: ExpandAll[(a + b)(a - b) / ((c + d)(c - d))]

Use Factor, Numerator, and Denominator to factor the numerator back:

Wolfram Language code: Factor[Numerator[#]] / Denominator[#]&[(a ^ 2 - b ^ 2) / (c ^ 2 - d ^ 2)]
Wolfram Research (1988), ExpandNumerator, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpandNumerator.html (updated 2007).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_expandnumerator, author="Wolfram Research", title="{ExpandNumerator}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ExpandNumerator.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_expandnumerator, organization={Wolfram Research}, title={ExpandNumerator}, year={2007}, url={https://reference.wolfram.com/language/ref/ExpandNumerator.html}, note=[Accessed: 13-June-2026]}