The Binomial Theorem is a formula which we can use to expand expressions , we generally use the notation (a) and (b) to stand for any numbers (or variables), and (n) to be any nonnegative integer.

In words, it tells us how to write the power of a binomial-a two-term expression-as a sum of terms. Every term in the expansion consists of a coefficient called a binomial coefficient-and a power of (a) combined with a power of (b).

This theorem provides an exact method of how many ways we can pick terms from the binomial and how their exponents can change when we expand it. It is appropriately applied in every domain in mathematics, namely in algebra, probabilities, and combinatorics.  

Formula For Binomial Theorem

The formula is given as ,

  

where n! the product of all the whole numbers between 1 to n.

Binomial Theorem Application

Q.1: Find the value of        .

Solution

        = 10! / (10 – 6)! 6!

10! / 4! 6!

Q.2: Expand

 

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