# Binomial Theorem

**Binomial Theorem**

In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power (*x* + *y*)^{n} into a sum involving terms of the form *ax*^{b}*y*^{c}, where the exponents b and c are nonnegative integers withb + c = n, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

1.Binomial theorem is heavily used in probability theory, and a very large part of the US economy depends on probabilistic analyses.it is most useful in our economy to find the chances of profit and loss which done great deal with developing economy.

2.Binomial theorem and distribution is used in higher mathematics and calculation.suppose you have given an equation with have degree 28 i.e like

(2x)^{28}+(3x)^{27}..................................+2x +3. you can find here all 28 roots of x.In certain scientific research binomial is very helpful to solve impossible equations.if you have seen Einstein equations there is a lot use of binomial theorem. that's why we have now very great theories and laws by sir Albert Einstein.

3.Moreover binomial theorem is used in forecast services .the future weather forecasting is impossible without binomial theorem.the disaster forecast is also depend upon binomial theorems.

4.The selection is the most using application in our life.popularly known it uses this theorem to giving ranks to the candidate..

5.The probability will impossible without binomial distribution.

6.It is used in architecture to giving shape and determining the areas of infrastructure to find about the amount of material to be use in that. it help in the estimation and to find the total expenditure to build the building .so all financial sites depend indirectly on binomial theorem

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top. The entries in each row are numbered from the left beginning with k = 0 and are usually staggered relative to the numbers in the adjacent rows