Find the coefficient of x^{5} in the expansio | vedclass

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Question

(A) The general term $(T_{r+1})$ in the binomial expansion of $(a+b)^{n}$ is given by $T_{r+1} = {}^{n}C_{r} a^{n-r} b^{r}$.For the expansion $(x+3)^{

Vedclass · Accepted Answer

$1512$

Vedclass · Answer

(A) The general term $(T_{r+1})$ in the binomial expansion of $(a+b)^{n}$ is given by $T_{r+1} = {}^{n}C_{r} a^{n-r} b^{r}$.For the expansion $(x+3)^{8}$,we have $n=8$,$a=x$,and $b=3$.Thus,$T_{r+1} = {}^{8}C_{r} x^{8-r} 3^{r}$.To find the coefficient of $x^{5}$,we set the exponent of $x$ equal to $5$:$8-r = 5 \implies r = 3$.Substituting $r=3$ into the general term expression:Coefficient $= {}^{8}C_{3} 	imes 3^{3} = \frac{8 	imes 7 	imes 6}{3 	imes 2 	imes 1} 	imes 27 = 56 	imes 27 = 1512$.

Find the coefficient of $x^{5}$ in the expansion of $(x+3)^{8}$.

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