What is the 4th term in expansion of (1-5x)^3?

1 Answer
May 26, 2018

Fourth term is-1250x^3

Explanation:

We will use Binomial expansion of (1+y)^3; where y=-5x

By Taylor series,
(1+x)^n= 1+nx+(n(n+1))/(2!)x^2+(n(n+1)(n+2))/(3!)x^3+.......

So, Fourth term is(n(n+1)(n+2))/(3!)x^3

Substituting n=3 and xrarr -5x

:.Fourth term is(3(3+1)(3+2))/(3!)(-5x)^3

:.Fourth term is(3xx4xx5)/(6)(-5x)^3

:.Fourth term is10xx-125x^3

:.Fourth term is-1250x^3