Binomial Theorem Formula

If you want to expand a binomial expression with some higher power, then Binomial theorem formula works well for it. Following is the Binomial theorem formula:

(x + y)n = nΣr=0 nCr xn – r · yr

where, nCr = n!⁄(n-r)!r!

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

For Example 5! = 1 x 2 x 3 x 4 x 5.

Binomial Theorem Example

Q1) Find the value of 10C6 ?

10C6 = 10 ! / (10 – 6)! 6! = 10! / 4! 6! = (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10) / 1 x 2 x 3 x 4 x 1 x 2 x 3 x 4 x 5 x 6 = 7 x 8 x 9 x 10 /1 x 2 x 3 x 4 = 7 x 3 x 10 = 210

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