Determine the constant term in the expansion of (x+2)^9

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The constant term of a binomial expansion of nth order `(x+a)^n` is iven by `a^n` .

Therefore the constant term  `= 2^9`

                                          `= 512`

Therefore the constant term of `(x+2)^9` is 512.

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The binomial expansion states `(a+b)^n=sum_(k=0)^n(nCk)a^(n-k)b^k`

In our case `(x+2)^9=sum_(k=0)^9(9Ck)x^(9-k)2^k`

The only term without x will be when k=9 => x^0=1. Hence that term will be equal to `9C9*1*2^9=1*1*512=512`

So the only constant is 512

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