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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 ...
A stronger notion is polynomial expansion, meaning that the function f used to bound the edge density of shallow minors is a polynomial.If a hereditary graph family obeys a separator theorem, stating that any n-vertex graph in the family can be split into pieces with at most n/2 vertices by the removal of O(n c) vertices for some constant c < 1, then that family necessarily has polynomial ...
Wren & Martin refers to a single book High School English Grammar and Composition or collectively, a series of English grammar textbooks written jointly by P. C. Wren and H. Martin. [1] Written primarily for the children of British officers residing in India , these books were widely adopted by Indian and Pakistani schools in the post-colonial ...
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point.
Elementary algebra, also known as high school algebra or college algebra, [1] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 2 ] whilst algebra introduces variables (quantities without fixed values).
In mathematics, a trinomial expansion is the expansion of a power of a sum of three terms into monomials. The expansion is given by The expansion is given by ( a + b + c ) n = ∑ i , j , k i + j + k = n ( n i , j , k ) a i b j c k , {\displaystyle (a+b+c)^{n}=\sum _{{i,j,k} \atop {i+j+k=n}}{n \choose i,j,k}\,a^{i}\,b^{\;\!j}\;\!c^{k},}