Search results
Results from the WOW.Com Content Network
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 ...
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
This proof of the multinomial theorem uses the binomial theorem and induction on m.. First, for m = 1, both sides equal x 1 n since there is only one term k 1 = n in the sum. For the induction step, suppose the multinomial theorem holds for m.
The binomial approximation for the square root, + + /, can be applied for the following expression, + where and are real but .. The mathematical form for the binomial approximation can be recovered by factoring out the large term and recalling that a square root is the same as a power of one half.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
January 5, 2025 at 5:13 PM Prior to signing the bill, Biden touted the importance of Social Security benefits for working class Americans and said he was "proud to have played a small part in this ...
Oregon and Ohio State met this season in the Big Ten. Now they meet in the College Football Playoff. Our experts make their picks for the Rose Bowl.
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 .