The general term T_{r+1} in the binomial expansion is given by T_{r+1} = ^{n }C _{r} a^{n-r} b^{r}

Here x^{5} is the T_{r+1} term so a= x, b = 3 and n =8

T_{r+1} = ^{8}C_{r} x^{8-r} 3^{r}…………… (i)

For finding out x^{5}

We have to equate x^{5}= x^{8-r}

⇒ r= 3

Putting value of r in (i) we get

\(T_{3+1}= ^8C_3x^{8-3}3^3\)

\( T_4=\dfrac{8!}{3!5!}\times x^5\times 27\)

= 1512 x^{5}

Hence the coefficient of x^{5}= 1512

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