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In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition. Expansion of a polynomial expression can be obtained by repeatedly replacing subexpressions that multiply two other subexpressions, at least one of which is an addition, by the equivalent sum of products, continuing until the expression becomes a ...
Microsoft Excel is a spreadsheet editor developed by Microsoft for Windows, macOS, Android, iOS and iPadOS.It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications (VBA).
Similarly, the Laplace expansion along the j th column is the equality = = +,,. (Each identity implies the other, since the determinants of a matrix and its transpose are the same.) The coefficient ( − 1 ) i + j m i , j {\displaystyle (-1)^{i+j}m_{i,j}} of b i , j {\displaystyle b_{i,j}} in the above sum is called the cofactor of b i , j ...
Over the next two years, the station continued to expand. A Soyuz-U rocket delivered the Pirs docking compartment . The Space Shuttles Discovery , Atlantis , and Endeavour delivered the American Destiny laboratory and Quest airlock , in addition to the station's main robot arm, the Canadarm2 , and several more segments of the Integrated Truss ...
The NSA has been reported to have access to all communications made via Google, Microsoft, Facebook, Yahoo, YouTube, AOL, Skype, Apple and Paltalk, [298] and collects hundreds of millions of contact lists from personal email and instant messaging accounts each year. [299]
Joe Biden's tenure as the 46th president of the United States began with his inauguration on January 20, 2021, and ended on January 20, 2025. Biden, a member of the Democratic Party who previously served as vice president for two terms under President Barack Obama from 2009 to 2017, took office after his victory in the 2020 presidential election over the incumbent president, Donald Trump of ...
Starlink is a satellite internet constellation operated by Starlink Services, LLC, an international telecommunications provider that is a wholly owned subsidiary of American aerospace company SpaceX, [5] providing coverage to over 100 countries and territories.
Historical Hilgenberg globes [1] Potential reconstruction of continents bordering the Atlantic (left column) and Pacific (right column) oceans as they might have appeared at different points, going back in history, using the expanding Earth hypothesis, based on reconstructions by expanding Earth proponent Neal Adams