binomial expansion

USAGE SUMMARY

The phrase "binomial expansion" is correct and usable in written English.
It is typically used in mathematics to refer to the expansion of expressions that are raised to a power, specifically in the context of the binomial theorem. Example: "The binomial expansion of (a + b)² is a² + 2ab + b²."

✓ Grammatically correct

Science

Encyclopedias

News & Media

Human-verified examples from authoritative sources

Exact Expressions

32 human-written examples

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

Encyclopedia Britannica

Learners taught with UZWEBMAT took end-of-subject tests for permutation, combination, binomial expansion and probability containing 20, 20, 15 and 20 questions respectively.

Expert Systems with Applications

As the intermediate G. ruber (W) pairs are interchangeable amongst coeval couplets (their transitional form inhibits selective categorization), we generated all possible combinations of the couplets in each archive using binomial expansion (See Methods for details).

Nature

The number of unique combinations n possible for a given number of samples s in an archive is obtained by binomial expansion: After generating n combinations, we computed the mean (μc) and standard deviation (σc) of the offsets for each combination.

Nature

The chapter also focuses on four commercially available modeling approaches to the analysis of portfolio credit risk: Moody's Investors Service's Binomial Expansion Technique (BET), J.P. Morgan/RiskMetrics Group's Credit-Metrics model, Moody's KMV's KMV model, and Credit Suisse Financial Products CreditRiskk+ model.

Understanding Credit Derivatives and Related Instruments

With binomial expansion, we have (32).

EURASIP Journal on Wireless Communications and Networking

Human-verified similar examples from authoritative sources

Similar Expressions

28 human-written examples

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

Using the binomial expansions of the expressions begin{array}rcl@ left[!1-left(!1- theta/x)^{alpha}!right) left(!1- theta/xtheta/x)^{alpha}!right) !right]^{b-1}, quad left(!1+lambda/x)^{alpha}!rightheta/x1)a-1}~~ text{and} quad left(1+lambda (theta/x)^{alpha}right)^{(k+1)a-1}, end{aright.

Journal of Statistical Distributions and Applications

Since not all SNPs are biallelic, binomial expansions of the equation were used to compute expected values.

British Journal of Cancer

This e-learning system was intended for learning and teaching secondary school level permutation-combination-binomial expansion and probability subjects.

Expert Systems with Applications

Then, each factor of product is fractionalized by taking fractional power and using binomial series expansion.

Signal Processing

Expert writing Tips

Best practice

When using "binomial expansion", ensure that the context clearly involves a binomial expression raised to a power. This term is specifically used in algebra and calculus.

Common error

Avoid using "binomial expansion" in non-mathematical contexts. The phrase has a specific mathematical meaning, and using it elsewhere may cause confusion.

Linguistic Context

The phrase "binomial expansion" functions primarily as a mathematical noun phrase. It denotes a specific mathematical operation: the expansion of a binomial expression raised to a power. Ludwig provides examples of its usage in mathematical and scientific contexts.

Expression frequency: Uncommon

Frequent in

Science

73%

Encyclopedias

8%

Academia

8%

Less common in

News & Media

5%

Wiki

3%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, "binomial expansion" is a mathematical term referring to the expansion of a binomial expression to a power. Ludwig confirms that the phrase is grammatically correct and usable in written English, primarily within mathematical and scientific contexts. While the phrase is most often used in science, it also has occurrences in encyclopedias and academia. When writing, ensure that you are using "binomial expansion" in the correct mathematical context to avoid confusion. For alternative phrasing, consider "binomial theorem expansion" or "expansion of a binomial".

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

binomial theorem expansion

Specifies the use of the binomial theorem to perform the expansion.

expansion using binomial theorem

Highlights that the expansion is achieved by applying the binomial theorem.

binomial series expansion

Indicates the expansion results in a binomial series.

expansion of a binomial

A more general term that refers to the process of expanding a binomial expression.

developing binomial expressions

Focuses on the process of developing or calculating the expanded form of binomials.

algebraic expansion of binomials

Emphasizes the algebraic nature of the expansion.

power series expansion of binomials

Describes the expansion as a power series.

applying the binomial formula

Focuses on the use of the binomial formula in the expansion process.

calculating binomial expansions

Highlights the computational aspect of finding the expansion.

determining the binomial expansion

Refers to finding or identifying the full expansion of a binomial expression.

FAQs

How is "binomial expansion" used in mathematics?

In mathematics, "binomial expansion" refers to the expansion of a binomial expression raised to a power, typically using the binomial theorem. For example, the "binomial theorem expansion" of (a + b)² is a² + 2ab + b².

What's the difference between "binomial expansion" and the binomial theorem?

"Binomial expansion" is the process or result of expanding a binomial expression, while the binomial theorem is the theorem or formula used to perform that expansion. The "binomial theorem" provides a general formula for the expansion.

What are some alternatives to "binomial expansion"?

Depending on the context, you could use alternatives like "expansion using binomial theorem" or "binomial series expansion". if you want to simply mention the "expansion of a binomial".

Where can I find examples of "binomial expansion" in use?

Examples of "binomial expansion" are commonly found in textbooks, academic papers, and online resources related to algebra, calculus, and combinatorics. You might also find it discussed in contexts related to probability and statistics where binomial distributions are used.