expansion using binomial theorem

USAGE SUMMARY

The phrase "expansion using binomial theorem" is correct and usable in written English.
You can use it in mathematical contexts when discussing the process of expanding expressions based on the binomial theorem. Example: "In algebra, we often encounter expressions that require expansion using binomial theorem to simplify calculations."

✓ Grammatically correct

Science

Science & Research

Encyclopedias

Human-verified similar examples from authoritative sources

Similar Expressions

60 human-written examples

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 expressions in (9) and (10) can be obtained by using binomial expansion at first which results the term with power series raised to power ∑ i = 0 ( L B - 1 ) 1 i ! ( γ B γ ̄ B ) i m.

EURASIP Journal on Wireless Communications and Networking

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

Signal Processing

Confidence intervals in the observed prevalence were estimated by using binomial approximation.

Nature

Comparisons of single proportions to hypothesized null values were evaluated using binomial tests.

Nature

Using binomial coefficients the Clebsch-Gordan and Gaunt coefficients were calculated for extremely large quantum numbers.

Journal of Computational Physics

where (38) is obtained by using the binomial theorem and the help of (19).

EURASIP Journal on Wireless Communications and Networking

Thus, for example, in the case of the fluent z = xn, Newton first forms z· + z·o = (x· + x·o)n, expands the right-hand side using the binomial theorem, subtracts z = xn, divides through by o, neglects all terms still containing o, and so obtains z· = nxn−1 x·.

SEP

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

Britannica

Recalling that for all g ≥ 0, s1, g + s2, g + h g = 1, h0 = 0, and for all g ≥ 2, H 1, g − 1 (1 ) and H 1, g − 1 (2 ) are IID random variables, we can use the binomial theorem to obtain a simplified recursion for the moments of H1, g.

Genetics

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

Encyclopedia Britannica

Expert writing Tips

Best practice

When discussing mathematical proofs or derivations, clearly specify which terms you are expanding using the binomial theorem to avoid ambiguity. For example, "The expression (1+x)^n was expanded using the binomial theorem."

Common error

Avoid assuming the binomial theorem applies to all polynomial expansions. The binomial theorem specifically applies to expressions of the form (a + b)^n. If your expression is more complex, other expansion techniques may be required.

Linguistic Context

The phrase "expansion using binomial theorem" functions as a noun phrase, often used in mathematical and scientific contexts. It describes the process of applying the binomial theorem to expand a mathematical expression. Ludwig AI confirms that the phrase is usable in written English.

Expression frequency: Missing

Frequent in

Science

33%

Science & Research

33%

Encyclopedias

33%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "expansion using binomial theorem" is a grammatically sound and technically accurate way to describe the process of expanding a mathematical expression using the binomial theorem. While Ludwig AI validates its usability, it's predominantly found in scientific, academic, and encyclopedic contexts. Given its specificity, more common alternatives include "binomial theorem expansion" or simply "applying the binomial theorem". When using this phrase, ensure clarity and precision in specifying which expressions are being expanded to avoid ambiguity. Due to its lack of examples in the search data, its real-world frequency is hard to determine.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

binomial theorem expansion

Reorders the words for brevity, emphasizing the theorem itself.

application of the binomial theorem

Focuses on the application aspect rather than the expansion process.

binomial expansion method

Highlights the methodological aspect of the binomial expansion.

using binomial series expansion

Specifies the series expansion involved in the binomial theorem.

application of binomial expansion

Shortened form that focuses on the result of the binomial theorem.

binomial theorem application

Inverts the original term focusing in the theorem instead of the usage of it.

applying the binomial theorem for expansion

Emphasizes the active process of applying the theorem.

utilizing binomial theorem for expansion

Replaces "using" with "utilizing", indicating a more formal tone.

carrying out binomial expansion

Highlights the execution of the expansion process.

the process of binomial expansion

More descriptive, framing it as a specific process.

FAQs

How can I describe the "expansion using binomial theorem" in simpler terms?

You can say "applying the binomial theorem", or "using binomial expansion" depending on the context. Both phrases refer to the process of expanding a binomial expression raised to a power.

What is the difference between "expansion using binomial theorem" and "binomial theorem expansion"?

The phrase "expansion using binomial theorem" describes the act of expanding an expression using the theorem, while "binomial theorem expansion" is a noun phrase referring to the result of applying the theorem. Both are valid but have slightly different emphasis.

In what situations is "expansion using binomial theorem" most applicable?

This phrase is most appropriate when discussing mathematical derivations, proofs, or examples where the binomial theorem is explicitly used to expand an expression of the form (a + b)^n.

Are there alternative methods to "expansion using binomial theorem" for more complex expressions?

Yes, for more complex polynomial expressions, techniques like polynomial long division or other algebraic manipulations might be necessary. The binomial theorem is specifically tailored for binomial expressions raised to a power.