Find the coefficient of #x^3# in the expansion of #(1+3x)^8# ?

1 Answer
Jim G.
Dec 7, 2017

#1512#

Explanation:

#"using the "color(blue)"binomial theorem"#

#•color(white)(x)(a+b)^n=sum_(r=0)^n((n),(r))a^(n-r)b^r#

#•color(white)(x)T_(r+1)=((n),(r))a^(n-r)b^r#

#"here "a=1" and "b=3x#

#rArrT_4=((8),(3))1^5(3x)^3#

#color(white)(xxxx)=56xx1xx27x^3#

#color(white)(xxxx)=color(red)(1512)x^3#

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