Binomial Theorem – Easy and Simple to Calculate Expressions with Larger Power

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A simple act of tossing a coin can have two possible outcomes: Heads or Tails. Have you ever wondered what is the mathematics involved behind this simple outcome? It’s Binomial Distribution which can be explained in a better sense by Binomial Theorem.

The Binomial Theorem is the way of expanding expressions that have non-negative power. As the power increases the expression becomes lengthy and tough to solve but with the help of the Binomial theorem, it becomes very easy and simple to calculate expressions with larger power. Learning Binomial theorem in maths online classes is fun. 

How to Define Binomial Theorem?

Bi means two and poly mean many hence Binomial contains only two terms (like a and b) while a polynomial contains many terms (like a, b, c, d….etc). We can also say that a Binomial is a Polynomial consisting of only two terms.

A Binomial can be written as (a+b), now what if we want to multiply (a+b) with itself, we get: –

(a+b) (a+b) = a^2 + 2ab + b^2[1] 

Now, what will happen if we multiply above resulting expression and once again multiply with (a+b): –

(a^2 + 2ab + b^2) (a+b) = a^3 + 3a^2b + 3ab^2 + b^3

And again

(a^3 + 3a^2b + 3ab^2 + b^3) (a+b) = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4

We can go on multiplying as long as we want. We shall notice that we are following some kind of pattern and if we summed up the pattern we shall arrive at our Binomial Theorem.

Binomial Theorem in Daily Life

Now as with the use of all other mathematical formulae we wonder what the practical usage of the Binomial Theorem in the real-world is. Binomial Theorem has the following real-world application: –

  • Distribution of Internet Protocol Address

Internet Protocols also abbreviated as IPs of our computer are automatically generated and distributed using Binomial Theorem. This method of generating and distributing the IP’s of the computer is also known as variable subnetting.

  • National Economic Prediction

Prediction mostly involves statistical probability. As predicting the economy involves numerous external and internal variables. Binomial Theorem can be used in predicting the nation’s future.

  • Architecture

Projects which involve complex measurement and calculation such as estimating the cost in engineering projects. Time taken to complete the construction of the structure and material needed to build a structure.

  • Weather Forecasting

Similar to prediction, forecasting involves probability. As there are numerous variables involved in forecasting the weather. The Binomial theorem can be of great help to us in this scenario also.

  • In Higher Mathematics and Calculation

Binomial Equation is used to find the roots of the equation of higher power, to derive and 

prove important equations in mathematics as well as physics. Binomial Theorem can make our life is easy.

Basically, the Binomial Theorem can be used to calculate probability and expected values.

Benefits of Maths Online Classes

With the advent of the pandemic, almost all the teaching and learning has been shifted online.  Following are the benefits one gets with Math online classes via platforms like cuemath: –

  • Learning From Home Sweet Home 

There’s no comfort like home. Online Math classes can help you study from the comfort of your home.

  • Save Time and Money 

When you opt to study from home (Online classes), you save a lot of travelling time that can be used in practicing or revising the content. Online classes also let you save money on travel as you don’t need to take a bus or cab to reach your classes.

  • Best Maths Experts 

Online classes give you an option to learn from the subject experts.

  • Instant Doubt Solving 

Online tutoring platforms let you solve your doubts instantly and you don’t have to wait till the class gets over.

And you get all the above mentioned benefits when you join cuemath Live classes. To understand some more facts about Binomial Theorem, visit

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