multinomial

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multinomial

A student writes a multinomial on the chalkboard.

Definition

  1. Adjective:

    • Having the character of a polynomial: Describes an expression or function that is structured as a sum of multiple terms, each consisting of a constant multiplied by one or more variables raised to non-negative integer powers.

  2. Noun:

    • A mathematical function that is the sum of a number of terms: A formal sum of terms, each of which is a product of a constant coefficient and one or more variables raised to powers. It is a generalization of a polynomial that may involve multiple variables.
Examples of Usage

  • Adjective:

    • The expression 3x²y + 2xy - 7 is a multinomial expression.
    • We simplified the multinomial equation before solving it.

  • Noun:

    • The expansion of (x + y + z)³ results in a multinomial with several terms.
    • In algebra, a multinomial can have more than one variable.
Advanced Usage

  • "Multinomial Theorem": A theorem that generalizes the binomial theorem, describing the expansion of a power of a sum into a sum of multinomial terms.

    • The Multinomial Theorem is essential for finding coefficients in complex expansions.

  • "Multinomial Coefficient": A coefficient that appears in the multinomial theorem, representing the number of ways to partition a set of objects into subsets of specified sizes.

    • Calculate the multinomial coefficient for the term x²y³z in the expansion.
Variants and Related Words

  • Polynomial (n/adj): A special case of a multinomial, typically referring to an expression with one variable or used more narrowly in some contexts. While all polynomials are multinomials, not all multinomials are called polynomials in every context.

    • A quadratic equation is a type of polynomial.

  • Binomial (n/adj): An expression consisting of exactly two terms.

    • (x + 5) is a simple binomial.
Synonyms
  • Polynomial (when used as a noun in a general sense).
  • Algebraic expression (a broader, less specific term).
Related Phrases
  • "Multinomial distribution": In probability theory and statistics, a generalization of the binomial distribution that describes the outcomes of a multi-category experiment.
    • The multinomial distribution models the probability of counts for rolling a die multiple times.
Related Idioms

(This term is technical and does not have common idiomatic expressions.)

multinomial

A student writes a multinomial on the chalkboard.

Adjective
  1. having the character of a polynomial
    • a polynomial expression
Noun
  1. a mathematical function that is the sum of a number of terms

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