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

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Answer 1 · 2018-05-26T09:44:21

Fourth term is#-1250x^3#

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 is#10xx-125x^3#

#:.#Fourth term is#-1250x^3#