How do you use the binomial formula to find the coefficient of #x^3# in #(3x^2 - (5/x))^3#?

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Answer 1 · 2016-09-28T20:17:19

#"The reqd. co-eff.="-135.#

In the expansion of #(a+b)^n#, the #(r+1)^(th)# term, i.e., #T_(r+1)# is,

#T_(r+1)=""_nC_ra^(n-r)b^r#.

In our Problem, we have, #a=3x^2, b=-5/x, and, n=3.# So,

#T_(r+1)=""_3C_r(3x^2)^(3-r)(-5/x)^r#.

#=(-5)^r""_3C_r(3)^(3-r)x^(6-2r)x^-r#.

#=(-5)^r(3)^(3-r)""_3C_rx^(6-3r)#

Hence, if #T_(r+1)# is the term containing #x^3#, we must have,

#6-3r=3 rArr r=1#

Therefore, the reqd. co-eff. is

#(-5)^1(3)^(3-1)""_3C_1=-5*9*3=-135.#

Enjoy Maths.!