Easy method to derive binomial expansion formula

You should have been wondering that binomial expansion formula was just written in most of the textbooks without proving it. So in this tutorial, I will explain how the formula was derived.

Now, let's start the tutorial.

There are many methods to prove it but I will consider using a simple method which will be well explanatory for those with little knowledge of mathematics.

By considering this below equation,

The first thing to do is differentiating it, is it strange? calm down, let me explain how to differentiate first, we just need basic knowledge..

I believed you've known how to differentiate now.

Let's proceed,

Putting x=0 in equation 1 to 5.

Equation 1 can be rewritten as,

Substituting a, b, c, d and e values in eq1

Now, let's derive an expression for binomial expansion.

Putting x=0 in eq 7 to 11

Lastly, substitute f'(0),f"(0),f'"(0) and f""(0) values in equation 6
Then we have,

You can see that the equation has been derived.

Reference

Quora-how to derive binomial expansion

I will explain how to derive an expansion for (a+b)^n in my next post

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