trevonknight2 trevonknight2
  • 17-05-2017
  • Mathematics
contestada

Find the coefficient of x^5y^8 in the expansion of (2x- y^2)^9
A 1200
B 4032
C 6543
D 1098

Respuesta :

WojtekR
WojtekR WojtekR
  • 17-05-2017
From binomial expansion we have, that:

[tex](2x-y^2)=\sum\limits_{k=0}^9\binom{9}{k}\cdot(2x)^{9-k}\cdot(-y^2)^k=\\\\\\= \dots+\binom{9}{4}\cdot(2x)^{9-4}\cdot(-y^2)^4+\dots=\\\\\\= \dots+\binom{9}{4}\cdot2^5x^5\cdot(-1)^4(y^2)^4+\dots= \dots+\binom{9}{4}\cdot2^5\cdot x^5y^8+\dots=\\\\\\=\dots+\dfrac{9!}{4!(9-4)!}\cdot32\cdot x^5y^8+\dots=\dots+\dfrac{9\cdot8\cdot7\cdot6}{4\cdot3\cdot2\cdot1}\cdot32\cdot x^5y^8+\dots=\\\\\\=\dots+126\cdot32\cdoy x^5y^8+\dots=\dots+\boxed{4032x^5y^8}+\dots[/tex]

Answer B.
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