Question

(PUC-PR) O coeficiente de x^5 no desenvolvimento de (x² - 4x +4)^4 é:
a) -12
b) -448
c) -8.945.664
d) -56
e) -2688

Answer 1

Resposta:

b) -448

Explicação passo a passo:

$(x^2 -4x + 4)^4\\ \\ (fatorando...) \\ \\ ((x-2)(x-2))^4\\ \\ ((x - 2)^2)^4\\ \\ (x-2)^8$

$Termo \ Geral: \binom{8}{p}x^{8-p}.(-2)^p\\ \\ 8-p = 5\\ p = 3\\ \\ \binom{8}{3}x^{8-3}.(-2)^3\\\\ \frac{8.7.6.5!}{(8-3)!.3!}.x^{5}.(-8)\\\\ \\ \frac{8.7.6.5!}{5!.3!}.x^{5}.(-8)\\ \\ \bold{-448x^{5}}$