What is the importance of the binomial theorem?

The binomial theorem gives us the general formula for the expansion of (a+b)n for any positive integer n. It also enables us to determine the coefficient of any particular term of an expansion of (a+b)n.

What are the applications of binomial theorem?

The theorem and its generalizations can be used to prove results and solve problems in combinatorics, algebra, calculus, and many other areas of mathematics. The binomial theorem also helps explore probability in an organized way: A friend says that she will flip a coin 5 times.

What is statement of binomial theorem?

Statement: Binomial theorem states that for any given positive integer n, the expression of the nth power of the sum of any two numbers a and b may take place as the sum of n+1 terms of the particular form.

How is binomial expansion used in real life?

It is used in architecture in 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.

What is binomial theorem in discrete mathematics?

The Binomial Theorem shows how to expand any whole number power of a binomial — that is, (x + y)n — without having to multiply everything out the long way. This square represents the identity (a + b)2 = a2 + 2ab + b2 geometrically. The Binomial Theorem shows how to expand any power.

How are Binomials used in real life?

Many instances of binomial distributions can be found in real life. For example, if a new drug is introduced to cure a disease, it either cures the disease (it’s successful) or it doesn’t cure the disease (it’s a failure). If you purchase a lottery ticket, you’re either going to win money, or you aren’t.

What is the biggest source of errors in the Binomial Theorem?

The biggest source of errors in the Binomial Theorem (other than forgetting the Theorem) is the simplification process. Don’t try to do it in your head, or try to do too many steps at once.

Who contributed the binomial theorem?

Isaac Newton
Isaac Newton is generally credited with the generalized binomial theorem, valid for any rational exponent.