binomial

Thân thiện

A biologist writes the binomial name for a butterfly in her notebook.

Definition

1. Adjective:

   • Having or characterized by two names, especially in scientific classification: Used to describe a naming system that uses two terms, typically the genus and species in biology.
   • Consisting of or relating to two algebraic terms: Used in mathematics to describe an expression containing two terms.

2. Noun:

   • A mathematical expression with two terms: An algebraic expression that is a sum or difference of exactly two monomials.

Usage Examples

• Adjective:

  • The scientist used the binomial system to classify the newly discovered insect.
  • (a + b) is a simple binomial expression.

• Noun:

  • In algebra, students learn to expand binomials like (x + 3)^2.
  • The square of a binomial always produces a trinomial.

Advanced Usage

• Binomial theorem: A fundamental theorem in algebra that describes the algebraic expansion of powers of a binomial.

  • The binomial theorem provides a formula for expanding expressions like (x + y)^n.

• Binomial distribution: A common probability distribution in statistics that summarizes the likelihood of a value taking one of two independent states.

  • The probability of getting a certain number of heads in coin flips follows a binomial distribution.

Variants and Related Words

• Binomial nomenclature (n): The formal system of naming species with two-part names (genus and species).

  • Carl Linnaeus established binomial nomenclature for organisms.

• Trinomial (adj/n): Consisting of or relating to three names or terms. (The logical extension beyond 'binomial').

Synonyms

• Two-term (adj): Consisting of two parts or terms.
• Dual (adj): Comprising two parts, elements, or aspects. (More general, not specific to math or taxonomy).

Related Phrases

• Binomial coefficient: A coefficient in the binomial theorem, often written as n choose k.

  • The binomial coefficients form the pattern known as Pascal's Triangle.

• Binomial expansion: The result of expanding an expression that is raised to a power.

  • Finding the binomial expansion of (1 + x)^5 is a standard exercise.

Học thuật

Adjective

1. having or characterized by two names, especially those of genus and species in taxonomies
   • binomial nomenclature of bacteria
2. of or relating to or consisting of two terms
   • binomial expression

Noun

1. (mathematics) a quantity expressed as a sum or difference of two terms; a polynomial with two terms

Từ đồng nghĩa

• binominal