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We often come across the algebraic identity (a + b)2 = a2 + 2ab + b2. In expansions of smaller powers of a binomial expressions, it may be easy to actually calculate by working out the actual product. But with higher powers the work becomes very cumbersome.

The binomial expansion theorem is a ready made formula to find the expansion of higher powers of a binomial expression.

Let ( a + b) be a general binomial expression. The binomial expansion theorem states that if the expression is raised to the power of a positive integer n, then,

(a + b)n = nC0an + nC1an-1 b+ nC2an-2 b2+ + nC3an-3 b3+ ………+ nCn-1abn-1+ + nCnbn

The coefficients in each term are called as binomial coefficients and are represented in combination formula. In general the value of the coefficient

nCr = n!r!(n-r)!

It may be interesting to note that there is a pattern in the binomial expansion, related to the binomial coefficients. The binomial coefficients at the same position from either end are equal. That is,

nC0 = nCn nC1 = nCn-1 nC2 = nCn-2 and so on.

The advantage of the binomial expansion theorem is any term in between can be figured out without even actually expanding.

Since in the binomial expansion the exponent of b is 0 in the first term, the general term, term is defined as the (r+1)th b term and is given by Tr+1 = nCran-rbr

The middle term of a binomial expansion is [(n/2) + 1]th term if n is even. If n is odd, then terewill be two middle terms which are [(n+1)/2]th and [(n+3)/2]th terms.

Q: What is binomial expansion theorem?

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The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.

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).

9! ~

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

What is the symbol for a Probability of success in a binomial trial?

Related questions

The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.

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).

universal binomial raised to power n means the is multiplied to itself n number of times and its expansion is given by binomial theorem

9! ~

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

First i will explain the 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,\.

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.