How do you find the sixth term of #(x-y)^9#?

1 Answer
Tazwar Sikder
May 25, 2017

#- 126 x^(4) y^(5)#

Explanation:

We have: #(x - y)^(9)#

Using the binomial theorem:

#= x^(9) + (""_1^9"") x^(8) (- y) + (""_2^9"") x^(7) (- y)^(2) + (""_3^9"") x^(6) (- y)^(3) + (""_4^9"") x^(5) (- y)^(4) + (""_5^9"") x^(4) (- y)^(5) + ...#

We only need to evaluate the sixth term of #(x - y)^(9)#:

#= x^(9) + (""_1^9"") x^(8) (- y) + (""_2^9"") x^(7) (- y)^(2) + (""_3^9"") x^(6) (- y)^(3) + (""_4^9"") x^(5) (- y)^(4) + underline ((""_5^9"") x^(4) (- y)^(5)) + ...#

#Rightarrow "Sixth term" = (""_5^9"") x^(4) (- y)^(5)#

#Rightarrow "Sixth term" = 126 cdot x^(4) cdot - y^(5)#

#Rightarrow "Sixth term" = - 126 x^(4) y^(5)#

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