Binominal Theorem
What are the fundamental concepts and applications of the binomial theorem in mathematics?
William P.
10. 05. 2024 12:09
1 odpověď
The binomial theorem expresses the expansion of , where a and b are terms and n is a non-negative integer.
The formula is:
where (binomial coefficient) is defined as:
These coefficients represent the number of ways to choose k items from n items.
They can be found in Pascal's triangle, where each entry is the sum of the two directly above it.
The sum of the coefficients of the expansion of is (setting a = b = 1).
One of many applications is expanding powers of binomials in algebraic manipulations and simplifications.
For example, calculating is possible without direct multiplication.