Ad
related to: simplifying and expanding brackets
Search results
Results from the WOW.Com Content Network
In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.
Square brackets are also often used in place of a second set of parentheses when they are nested—so as to provide a visual distinction. In mathematical expressions in general, parentheses are also used to indicate grouping (i.e., which parts belong together) when edible to avoid ambiguities and improve clarity.
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 ...
Another use of the Iverson bracket is to simplify equations with special cases. For example, the formula (,) = = is valid for n > 1 but is off by 1 / 2 for n = 1.To get an identity valid for all positive integers n (i.e., all values for which () is defined), a correction term involving the Iverson bracket may be added: (,) = = (() + [=])
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 ...
[5] [6] (Iverson used square brackets for a different purpose, the Iverson bracket notation.) Both notations are now used in mathematics, although Iverson's notation will be followed in this article. In some sources, boldface or double brackets x are used for floor, and reversed brackets x or ]x[for ceiling. [7] [8]
The equations simplify slightly when a system of quantities is chosen in the ... Expanding the divergence of the right ... is a vector; the square brackets, [ ], ...
Ad
related to: simplifying and expanding brackets