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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 form.

The Binomial Expansion Formula or Binomial Theorem is given as,

\[\large (x+y)^{n} = x^{n} + nx^{n-1}y + \frac{n(n-1)}{2!} x^{n-2} y^{2} + … + y^{n}\]

Solved Examples

Question 1: What is the value of (2+5)3 ?
Solution:
The binomial expansion formula is,
(x+y)n = xn + nxn-1y + $\frac{n(n-1)}{2!}$ xn-2y2 +…….+ yn
From the given equation,
x = 2 ; y = 5 ; n = 3
(2+5)3
= 23 + 3(22)(51) + $\frac{3 \times 2}{2!}$(21)(52) + $\frac{3 \times 2 \times 1}{3!}$(20)(53)
= 8 + 3(4)(5) + $\frac{6}{2}$(2)(25) + $\frac{6}{6}$(125)
= 8 + 60 + 150 + 125
= 343

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