Find the coefficient of \(\displaystyle x^6\) in the expansion \(\displaystyle (x + 3)^8\)

**My solution**

So: \(\displaystyle \sum_{i=0}^{8}\) \(\displaystyle \binom{8}{8-i}\) \(\displaystyle (x)^{8-i}\) \(\displaystyle (3)^i\)

now since we need to find coefficient of \(\displaystyle x^6\), therefore \(\displaystyle i = 6\).

so \(\displaystyle \binom{8}{2}\) \(\displaystyle (1)^2\) \(\displaystyle (3)^6\) = \(\displaystyle 28 \times 1 \times 739\) = \(\displaystyle 28 \times 739\)