binomial theorem expansion

USAGE SUMMARY

The phrase "binomial theorem expansion" is correct and usable in written English.
You can use it in mathematical contexts when discussing the expansion of expressions raised to a power, particularly in algebra. Example: "The binomial theorem expansion allows us to express (a + b)^n as a sum of terms involving binomial coefficients."

✓ Grammatically correct

Academia

Formal & Business

News & Media

Science

Encyclopedias

Wiki

Reference

Social Media

Human-verified similar examples from authoritative sources

Similar Expressions

60 human-written examples

For further mathematical detail, including an explicit formula for the kth term of a binomial expansion, see binomial theorem.

Encyclopedia Britannica

Thus, factorial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is defined as equal to 1. Factorials are commonly encountered in the evaluation of permutations and combinations and in the coefficients of terms of binomial expansions (see binomial theorem).

Britannica

Multinomial theorem, in algebra, a generalization of the binomial theorem to more than two variables.

Britannica

For example, Sir Isaac Newton used his binomial theorem to calculate 16 decimal places quickly.

Britannica

Now, by the binomial theorem, and I might add, the same binomial theorem that allowed us to get these results, we can also write that this is what?

Massachusetts Institute of Technology

(Consider "About binomial theorem I'm teeming with a lot o' news/With many cheerful facts about the square of the hypotenuse").

The New York Times

Covers set theory (integers, prime and rational numbers), algorithms (Euclidean, RSA encryption), theorems (Euler, Fermat, Chinese remainder), induction proofs (well-ordered sets, weak and strong induction), combinatorics (permutations, combinations, combinatorial proofs of the binomial theorem, Pascal's identity).

The New York Times

First-time Splash attendee ADITYA KRISHNAN took a math class on the binomial theorem.

Stanford University

In particular, the proof of the binomial theorem and the explanation of the method of finding square roots are of this character.

Nature

To establish these results, he introduced transformations among the variables of the problem, using a result equivalent to the binomial theorem for integral exponents.

Britannica

At home in 1666, he began to develop some of his most groundbreaking theories, including the generalized binomial theorem.

Massachusetts Institute of Technology

Expert writing Tips

Best practice

When discussing the "binomial theorem expansion", clarify the context by specifying the expression being expanded (e.g., "the binomial theorem expansion of (x + y)^n").

Common error

Avoid using "binomial theorem expansion" when you simply mean the binomial theorem itself. The expansion is the result, not the theorem.

Linguistic Context

The phrase "binomial theorem expansion" functions as a mathematical term describing the result of applying the binomial theorem to expand a binomial expression raised to a power. Ludwig provides examples of usage in mathematical and scientific contexts.

Expression frequency: Missing

Frequent in

Science

35%

Academia

30%

Encyclopedias

15%

Less common in

News & Media

10%

Wiki

5%

Formal & Business

5%

Ludwig's WRAP-UP

The phrase "binomial theorem expansion" refers to the process of expanding a binomial expression raised to a power using the binomial theorem. Ludwig confirms that this phrase is grammatically correct and usable, particularly in mathematical contexts. Although examples are currently limited, its use is prevalent in scientific and academic domains. The phrase effectively describes a mathematical operation and its result, often appearing in formal and scientific writing. Understanding its usage helps clarify explanations in mathematical and technical discussions.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

binomial expansion theorem

Reorders the words while retaining the core meaning.

expansion using binomial theorem

Focuses on the 'expansion' part and specifies the tool used.

binomial theorem's expansion

Uses a possessive form to link the theorem and the expansion.

expansion via the binomial theorem

Replaces "using" with "via", indicating the method used.

application of binomial theorem in expansion

Highlights the 'application' aspect of the theorem.

binomial series expansion

Emphasizes the series that results from the binomial theorem.

expanding with the binomial theorem

Uses a verb form to describe the action of expanding.

binomial theorem for expansion

Specifies the purpose of the binomial theorem.

the binomial theorem and its expansion

Explicitly mentions both the theorem and its resulting expansion.

how to expand using binomial theorem

Focuses on the procedural aspect of using the theorem.

FAQs

What is the purpose of the "binomial theorem expansion"?

The "binomial theorem expansion" is used to express powers of binomials (expressions with two terms) as a sum of terms, simplifying calculations and analysis.

How does the "binomial theorem expansion" relate to Pascal's triangle?

The coefficients in the "binomial theorem expansion" correspond to the numbers in Pascal's triangle, providing a visual and computational aid.

What are some practical applications of the "binomial theorem expansion"?

The "binomial theorem expansion" is used in probability, statistics, and various fields of engineering and physics to model and analyze complex systems. For example, can be used in queueing models like in probability theories

Is there a difference between "binomial expansion" and "binomial theorem expansion"?

While very similar, "binomial theorem expansion" explicitly refers to the process of expanding using the binomial theorem, while "binomial expansion" is a bit more general and can refer to the result of such expansion.