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$ k = 2 $: $ (-1)^2 \binom{5}{2} \cdot 3^8 = 1 \cdot 10 \cdot 6561 = 65610 $
$ k = 3 $: $ (-1)^3 \binom{5}{3} \cdot 2^8 = -1 \cdot 10 \cdot 256 = -2560 $
$ k = 4 $: $ (-1)^4 \binom{5}{4} \cdot 1^8 = 1 \cdot 5 \cdot 1 = 5 $
$ k = 5 $: $ (-1)^5 \binom{5}{5} \cdot 0^8 = -1 \cdot 1 \cdot 0 = 0 $
- 327680 = 62945 \\
+ 65610 = 128555 \\
- 2560 = 125995 \\
+ 5 = 126000 \\
+ 0 = 126000
$ k = 0 $: $ \binom{3}{0} \cdot 3^7 = 1 \cdot 2187 = 2187 $