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

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Solution

Here, general term of the expansion $(x + 3)^{8}$ is

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

Now $8 - r = 5 \Rightarrow r = 8 - 5 = 3$

$∴$ Putting r=3 in (i)

$T_{4} = 8_{C_{3}} x^{5} (3)^{3}$

$∴$ Coefficient of $x^{5}$ on the expansion

$(x + 3)^{8} = 8_{C_{3}} . (3)^{3} = 1512$

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