The coefficent of $x^{10}$ in the expansion $(x + 10)^{10}$

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Solution

Let $T r + 1 = n_{C_{r}} x^{n - r} x {(10)}^{r}$
Now $n = 10$ and $n - r = 10$
so, $r = 0$
$T r + 1 = 10_{C_{0}} x^{10} {(10)}^{0} = T_{1}$
So, coefficient $= 10_{C_{0}} \times {(10)}^{0} = 1$

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