Question

What is binomial theorem?

With its example and eq too?

Answer 1

Here is your answer user.

Answer 2

Actually I want to explain Binomial theorem in a simple way :-

An expression which is in the form of x + y is generally known as binomial theorem.

You can solve different equation by multiplication  like (x + y)^2 and (x + y)^3 and many more.

But when you will get expression like (x + y)^42.

You can solve it by using binomial theorem.

Maybe around 1660 B Pascal introduced a system of Pascal triangle. Which can solve (x + y)^n.

And in the same year Pascal gave the present form of Binomial theorem.

Check the attached pic for Pascal Triangle it will show you the coefficient of various term of binomial expansion.

For Non negative Integers :-

${\implies (x+y)^{0} = 1}$

${\implies (x+y)^{1} = x+y = {1}^C_{0}x + {1}^C_{1}y}$

Check the 2nd image you will get example.