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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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Q: What is the binomial theorem?
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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.


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".


Did Isaac newton co create the binomial theorem?

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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?

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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


How can you tell if a binomial divides evenly into a polynomial?

You can determine if a binomial divides evenly into a polynomial by using the remainder theorem or synthetic division. If the remainder is 0, then the binomial divides evenly into the polynomial.


What is the relationship between Pascal triangle and binomial theorem?

The coefficients of the binomial expansion of (1 + x)n for a positive integer n is the nth row of Pascal's triangle.