What is the coefficient of the term #x^6# in the expansion of #(x+3)^10#?

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Answer 1 · 2017-05-27T06:33:04

Coefficient of the term #x^6# in the expansion of #(x+3)^10# is #17010#.

In the expanssion od #(x+a)^n#

#(r+1)^(th)# term is #C_r^nx^(n-r)a^r#

Hence in the expanssion of #(x+3)^10#

#(r+1)^(th)# term is #C_r^10x^(10-r)3^r#

As we need coefficient of #x^6#, we have #10-r=6# or #r=4#

and coefficient is #C_4^10 3^4#

= #(10*9*8*7)/(1*2*3*4)xx81=210xx81=17010#