The general term Tr+1 in the binomial expansion is given by Tr+1 = n C r an-r br
Here x5 is the Tr+1 term so a= x, b = 3 and n =8
Tr+1 = 8Cr x8-r 3r…………… (i)
For finding out x5
We have to equate x5= x8-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 x5
Hence the coefficient of x5= 1512
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