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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 ...
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 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 .
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).
This template is a simple wrapper around the [ and ] HTML entities that produce starting and ending brackets, respectively. The template cannot output just an ending bracket. You will have to use ] to produce the "]" ending bracket. This template is not necessary in Citation Style 1 templates. You can simply use square brackets, and ...
The form comes with two worksheets, one to calculate exemptions, and another to calculate the effects of other income (second job, spouse's job). The bottom number in each worksheet is used to fill out two if the lines in the main W4 form. The main form is filed with the employer, and the worksheets are discarded or held by the employee.
[[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.
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
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