Distributive Property of Multiplication Over Addition and Subtraction
Pronunciation: /dɪsˈtrɪ.bjə.tɪv ˈprɒp.ər.ti ʌv ˌmʌl.tə.plɪˈkeɪ.ʃən ˈoʊ.vər əˈdɪ.ʃən ənd səbˈtræk.ʃən/ Explain
The distributive property of multiplication over addition and
subtraction states that a(b + c)
= ab + ac.^{[2]}
This property holds for
real numbers
and
complex numbers.
Click on the blue points in the figure and drag them to change the figure.
What happens if c is zero?

Manipulative 1  Distributive Property of Multiplication Over Addition and Subtraction Created with GeoGebra. 
References
 McAdams, David E.. All Math Words Dictionary, distributive property of multiplication over addition and subtraction. 2nd Classroom edition 201501084799968. pg 64. Life is a Story Problem LLC. January 8, 2015. Buy the book
 Fine, Henry B., Ph. D.. NumberSystem of Algebra Treated Theoretically and Historically. 2nd edition. pg 5. www.archive.org. D. C. Heath & Co., Boston, U.S.A.. 1907. Last Accessed 7/3/2018. http://www.archive.org/stream/thenumbersystemo17920gut/17920pdf#page/n14/mode/1up/search/distributive. Buy the book
 Jones, Burton. Elementary Concepts of Mathematics. pp 3841. www.archive.org. MacMillan and Company. 1947. Last Accessed 7/3/2018. http://www.archive.org/stream/elementaryconcep029487mbp#page/n59/mode/1up/search/distributive. Buy the book
 Keigwin, H. W.. Principles of Elementary Algebra. pg 7. www.archive.org. Ginn & Company. 1886. Last Accessed 7/3/2018. http://www.archive.org/stream/principlesofelem00dupurich#page/7/mode/1up. Buy the book
 Bettinger, Alvin K. and Englund, John A.. Algebra and Trigonometry. pg 3. www.archive.org. International Textbook Company. January 1963. Last Accessed 7/3/2018. http://www.archive.org/stream/algebraandtrigon033520mbp#page/n18/mode/1up. Buy the book
More Information
 McAdams, David E.. Distributive Property. lifeisastoryproblem.com. Life is a Story Problem LLC. 3/12/2009. http://www.lifeisastoryproblem.com/algebra/distributive.html.
Cite this article as:
McAdams, David E. Distributive Property of Multiplication Over Addition and Subtraction. 4/20/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/distributiveprop.html.
Image Credits
Revision History
4/20/2019: Updated equations and expressions to the new format (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
7/4/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (
McAdams, David E.)
1/24/2010: Added "References". (
McAdams, David E.)
7/11/2008: Add manipulative 1. (
McAdams, David E.)
7/12/2007: Initial version. (
McAdams, David E.)