How do you find the coefficient of #a# of the term #ax^4y^5# in the expansion of the binomial #(3x-2y)^9#?

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Answer 1 · 2018-01-28T16:03:15

#a = color(blue)(- 326592)#

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Pattern for power 9 as per Pascal's Triangle

1 9 36 84 126 126 84 36 9 1

#ax^4y^5# is the #6_th# term of the expansion.

#6_th# term is #126 (3x)^4(-2y)^5#

# = - 126 * (3)^4 x^4 (2^5) y^5#

#= - (126) * (81) * (32) x^4 y^5#

#= -(326592) x^4 y^5#

Hence #a = color(blue)(- 326592)#