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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 ...
This template inserts a square opening bracket [. Setting parameter 1 to 2 can be used to make it a double: {{Square bracket open|2}} → [[. Can be used to create a wikilink within a template, when using brackets directly might cause wrong parsing (since it can be read as an opening for a link).
[[Category:12-Team bracket templates]] to the <includeonly> section at the bottom of that page. Otherwise, add <noinclude>[[Category:12-Team bracket templates]]</noinclude> to the end of the template code, making sure it starts on the same line as the code's last character.
The trinomial expansion can be calculated by applying the binomial expansion twice, setting = +, which leads to (+ +) = (+) = = = = (+) = = = ().Above, the resulting (+) in the second line is evaluated by the second application of the binomial expansion, introducing another summation over the index .
As the exterior product is associative brackets are not needed as it does not matter which of a ∧ b or b ∧ c is calculated first, though the order of the vectors in the product does matter. Geometrically the trivector a ∧ b ∧ c corresponds to the parallelepiped spanned by a , b , and c , with bivectors a ∧ b , b ∧ c and a ∧ c ...
The acronym's procedural application does not match experts' intuitive understanding of mathematical notation: mathematical notation indicates groupings in ways other than parentheses or brackets and a mathematical expression is a tree-like hierarchy rather than a linearly "ordered" structure; furthermore, there is no single order by which ...
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Pages with many brackets or large brackets, especially those containing flag icons, may come close to or exceed Wikipedia's Post-expand include size limit. In these cases consider using modules directly instead: {{8TeamBracket}} can be replaced with {{#invoke:bracket|8TeamBracket}}.
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