Q. 13.7( 85 Votes )

# Find the coefficient of

x^{5} in (x + 3)^{8}

Answer :

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}……………1

For finding out x^{5}

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

⇒ r= 3

Putting value of r in 1 we get

T_{3+1} = ^{8}C_{3} x^{8-3} 3^{3}

= 1512 x^{5}

Hence the coefficient of x^{5}= 1512

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