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

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mathisgay | Student, Undergraduate | Honors

Posted May 10, 2012 at 6:24 PM via web

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

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rcmath | High School Teacher | (Level 1) Associate Educator

Posted May 11, 2012 at 2:54 AM (Answer #1)

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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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thilina-g | College Teacher | (Level 1) Educator

Posted May 29, 2012 at 6:36 PM (Answer #1)

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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.

Sources:

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baronridiculous | College Teacher | eNoter

Posted May 10, 2012 at 7:10 PM (Answer #2)

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The expansion would look like:

x^9 + ....... + 2^9

We only care about the last term:

2^9 = 512

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