It's better to think about the ordinary binomial theorem first.
Consider a binomial (x + y), and raising it to a power, say squaring it.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Now try cubing it.
(x + y)^3 = (x + y)(x + y)(x + y) = x^3 + 3x^2 y + 3xy^2 + y^3
It becomes very tedious to do this. The binomial theorem allows us to expand binomial expressions to a power very quickly.
The generalised binomial theorem is, as it says, 'generalised' - the 'original' binomial theorem only allows us to expand binomial expressions to a power which is a whole number (0, 1, 2, 3 ... etc) but not numbers such as 1/2, 1/3 or -1.
Newton's generalised binomial theorem allows us to expand binomial expressions for any _rational_ power. (that is any number which can be expressed as a ratio of two integers - not something horrible like the cube root of three)
So now we can expand things like (x + y)^0.5, (1 - x)^-1 and all that malarky - this has some fairly deep significances, such as allowing numerical approximations of surds and bears relevance to some power series.
For example, take (1 - x)^-4, using Newton's generalised binomial theorem it can be seen that
(1 - x)^-4 = 1 + 4x + 10x^2 + 20x^3 ...
Each expansion for a rational exponent of the binomial expressions creates an infinite series.
The actual calculations are best left to a site which can show you the mathematical notation, but if you can do the normal binomial theorem - the nuances of this one will be easy to grap.
Binomial expansions and the binomial theorem,\.
universal binomial raised to power n means the is multiplied to itself n number of times and its expansion is given by binomial theorem
In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalised binomial theorem, developed the so-called "Newton's method" for approximating the zeroes of a function. He used the methods of calculus to solve the problem of planetary motion.
being an epic scientist ~ Sir Isaac Newton made plenty of scientific discoveries- tough the most famous is gravity, he also discovered the Three Universal Laws of Motion, which was then made into basic Physics by him. This helped prove Copernicus's theory of the planets orbiting the Sun. He also made the Binomial Theorem and was one of the two creators of calculus. Ultimately, his discoveries were predecessors to discoveries made by the other great scientists, such as Einstein. -Ben ~
The skew binomial distribution arises when the probability of a particular event is not a half.
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
You don't, unless you work in engineering. The Wikipedia article on "binomial theorem" has a section on "Applications".
yes Isaac Newton created the binomial theorem
Binomial expansions and the 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).
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 symbol for a Probability of success in a binomial trial?
AnswerThe binomial theorem has been known for thousands of years. It may have first been discovered in India around 500 BC.
suck my balls
universal binomial raised to power n means the is multiplied to itself n number of times and its expansion is given by binomial theorem
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.
The coefficients of the binomial expansion of (1 + x)n for a positive integer n is the nth row of Pascal's triangle.