Noun
/mʌltɪˈnoʊmiəl ˈθiːoʊrɛm/
The multinomial theorem is a generalization of the binomial theorem that describes how to expand expressions that are raised to a power, particularly involving terms with more than two variables or terms. It provides a formula for expanding a power of a sum of multiple terms as a sum of products involving the coefficients determined by the multinomial coefficients. This theorem is particularly used in combinatorics and algebra.
The term "multinomial theorem" is used mainly in mathematical contexts, particularly in algebra and combinatorics. It is more frequently encountered in written contexts such as textbooks, research papers, and academic articles than in oral speech.
The multinomial theorem allows us to expand (x + y + z)³ into a sum of terms.
(El teorema multinomial nos permite expandir (x + y + z)³ en una suma de términos.)
In combinatorial mathematics, the multinomial theorem is used to determine the number of ways to distribute indistinguishable objects into different bins.
(En matemáticas combinatorias, el teorema multinomial se usa para determinar cuántas maneras hay de distribuir objetos indistinguibles en diferentes contenedores.)
Understanding the multinomial theorem is essential for solving complex probability problems.
(Entender el teorema multinomial es esencial para resolver problemas de probabilidad complejos.)
The term "multinomial theorem" does not have commonly used idiomatic expressions. However, it is frequently referenced in contexts involving algebra or combinatorial discussions. Below are similar expressions within mathematical contexts:
"With the multinomial expansion, we can easily calculate probabilities for multiple events."
(Con la expansión multinomial, podemos calcular fácilmente probabilidades para múltiples eventos.)
"Using the multinomial coefficients, we can find the number of ways different tasks can be assigned."
(Usando los coeficientes multinomiales, podemos encontrar el número de maneras en que se pueden asignar diferentes tareas.)
"The multinomial distribution provides a framework for modeling multi-category outcomes."
(La distribución multinomial proporciona un marco para modelar resultados de múltiples categorías.)
The term "multinomial" is derived from the Latin word "multus," meaning "many," combined with "nomial," which comes from the Latin "nomen," meaning "name" or "term." Thus, "multinomial" literally translates to "many terms," reflecting its use in algebra concerning multiple variables or terms.
In summary, the multinomial theorem is a fundamental concept within algebra that extends the applications of the binomial theorem to expressions involving multiple variables. It is crucial for various mathematical fields, especially those dealing with statistics and combinatorics.