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