Help on Binomial Theorem

Introduction to binomial theorem:

The binomial theorem explains the power of the binomial. Binomial coefficient is the resulting coefficient of the expression. By using binomial theorem we can raise the power. For example, (x+y) is a binomial.

Binomial Expansions:

This will also help us on angular velocity

(a + b)0 = 1

(a + b)1 = a + b

(a + b)2 = a2 + 2ab + b2

(a + b)3 = a3 + 3a2b + 3ab2 + b3

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4

(a + b)5 = a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

Binomial theorem helps us expand binomials to any given power without direct multiplication. Direct Multiplication can be time-consuming or even not possible in some cases.