Binomial Expansion Formula

The Binomial Expansion Theorem is an algebra formula that describes the algebraic expansion of powers of a binomial. According to the binomial expansion theorem, it is possible to expand any power of x + y into a sum of the terms.

The Binomial Expansion Formula or Binomial Theorem is given as:

(x+y)n=xn+nxn−1y+n(n−1)2!xn−2y2+…+yn

Solved Example

Question : What is the value of (2 + 5)3 ?
Solution:
The binomial expansion formula is,
(x + y)n = xn + nxn-1y +

n(n−1)2!
 xn-2y2 +…….+ yn
From the given equation,
x = 2 ; y = 5 ; n = 3
(2 + 5)3
= 23 + 3(22)(51) +
3×22!
(21)(52) +
3×2×13!
(20)(53)
= 8 + 3(4)(5) +
62
(2)(25) +
66
(125)
= 8 + 60 + 150 + 125
= 343

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