Write down the binomial expansion of `(1+x)^(n+1)` , when x=8. Deduce that `9^(n+1)-8n-9` is divisible by 64 where, `n` is a positive integer.

Explanation

`(x+a)^{n}=sum_{gamma=0}^{n}left(n_{c_{gamma}}right) x^{n-gamma} a^{gamma}`,


`n c_{r}=frac{n !}{r !(n-r) !}`
`(1+x)^{n+1}=n+1 c_{0} 1^{n+1} x^{0}+{ }^{n+1} c_{1} 1^{n+1-1}`
/,br>
`x^{1}+n+l_{c_{2}},{ }^{n+1-2} x^{2}`
`+cdots+n^{+1}(n+1)^{(n+1)}-(n+1) cdot(x+1)`


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