Find the constant term in the expansion of (4x^2 - 1/2x)^9 .
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2008-12-14 10:18 pm
回答 (1)
2008-12-14 10:43 pm
✔ 最佳答案
By binomial theorem:
(4x2 - 1/2x)9 = (4x2)9 - 9C1(4x2)8(1/2x) + ... + (-1)r9Cr(4x2)n-r(1/2x)r + ... -(1/2x)9
The constant term:
(x2)9-r•(1/x)r = xo
x18-2r•x-r = xo
x18-2r-r = xo
x18-3r = xo
18-3r = 0
r = 6
The constant term
= (-1)6•9C6(4x2)9-6(1/2x)6
= (1)(9!/6!3!)(4x2)3(1/2x)6
= 84(64x6)(1/64x6)
= 84
=
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