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In mathematics, the binomial theorem is an important formula giving the expansion of powers of sums. Its simplest version reads (x+y)^n=\sum_{k=0}^n{n \choose k}x^ky^{n-k}\quad\quad\quad(1) whenever n is any non-negative integer, the numbers {n \choose k}=\frac{n!}{k!(n-k)!} are the binomial coefficients, and n! denotes the factorial of n. This formula, and the triangular arrangement of the binomial coefficients, are often attributed to Blaise Pascal who described them in the 17th century. It was, however, known to Chinese mathematician Yang Hui in the 13th century. For example, here are the cases n = 2, n = 3 and n = 4: (x + y)^2 = x^2 + 2xy + y^2\, (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3\, (x + y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4.\, Formula (1) is valid for all real or complex numbers x and y, and more generally for any elements x and y of a semiring as long as xy = yx.
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What is a binominal theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
Did Isaac newton co create the binomial theorem?
yes Isaac Newton created the binomial theorem
How do you use binomial theorem in daily life?
You don't, unless you work in engineering. The Wikipedia article on "binomial theorem" has a section on "Applications".
How did Sir Isaac Newton contribute to algebra?
Binomial expansions and the binomial theorem,\.
Define binomial theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial: that is, the expansion of an expression of the form (x + y)^n where x and y are variables and n is the power to which the binomial is raised. When first encountered, n is a positive integer, but the binomial theorem can be extended to cover values of n which are fractional or negative (or both).
How can we use of binomial theorem in pharmacy?
Binomial Theorem consists of formulas to determine variables. In pharmacy it can be used to calculate risks and costs of certain medications.
What is the relationship between probability and the binomial theorem?
What is the symbol for a Probability of success in a binomial trial?
Who invented binomial theorem?
AnswerThe binomial theorem has been known for thousands of years. It may have first been discovered in India around 500 BC.
Why is the binomial theorem important for daily life?
suck my balls
Who created the binomial theorem?
The binomial theorem is attributed to several mathematicians throughout history, but it was most notably developed by Isaac Newton in the late 17th century. While the formula for expanding powers of a binomial expression had been known in simpler forms before him, Newton generalized it for any positive integer exponent. The theorem expresses the expansion of ((a + b)^n) as a sum involving binomial coefficients.
What is universal binomial raised to power n?
universal binomial raised to power n means the is multiplied to itself n number of times and its expansion is given by binomial theorem
Why do you need to study binomial theorem?
Studying the binomial theorem is essential because it provides a powerful method for expanding expressions of the form (a + b)^n, enabling efficient calculations in algebra and combinatorics. It lays the groundwork for understanding probabilities, as it relates to binomial distributions, which model various real-world scenarios. Additionally, the theorem enhances problem-solving skills and is applicable in calculus, making it a vital concept in higher mathematics.
