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Consider the expansion of (3x^2 - 1/x)^9.  Find the constant term in this expansion.

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lbawa | Student, Undergraduate | eNoter

Posted March 2, 2012 at 10:49 AM via web

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Consider the expansion of (3x^2 - 1/x)^9.  Find the constant term in this expansion.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 2, 2012 at 11:00 AM (Answer #1)

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Use the expansion (x + y)^n = `sum_(k=0)^n C(n, k) x^(n - k)*y^k`

The constant term for (3x^2 + 1/x)^9 is a term with no factors of x. This arrived at when `x^(18 - 2k)/x^k = 1`

=> 18 - 2k = k

=> 18 = 3k

=> k = 6

C(9, 6) = `(9!)/((6!)*(3!))` = `(9*8*7)/(3*2)` = 84

The constant term is 3^3*84 = 2268

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