Question

Qual é o coeficiente de x^6 na expansão de (2x+1)^8?
a) 1792
b) 16
c) 256
d) 1120
e) 1024

URGENTE!!!!!

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Termo~geral~do~bin\hat omio~de~Newton}\\\sf Dado~o~bin\hat omio~(a+b)^n~o~termo~geral\\\sf \acute e~dado~por~\sf T_{p+1}=\displaystyle\binom{\sf n}{\sf p}\cdot a^{n-p}\cdot b^p\end{array}}$

$\Large\boxed{\begin{array}{l}\sf T_{p+1}=\displaystyle\sf\binom{8}{p}\cdot (2x)^{8-p}\cdot 1^p\\\\\sf T_{p+1}=\displaystyle\binom{8}{p}\cdot 2^{8-p}\cdot x^{8-p}\\\sf para~obter~x^6~devemos~ter\\\sf 8-p=6\\\sf p=8-6\\\sf p=2\\\sf logo\\\sf T_{2+1}=\displaystyle\binom{8}{2}\cdot 2^{8-2}\cdot x^{8-2}\\\\\sf\displaystyle \sf T_3=28\cdot 2^6\cdot x^6\\\sf T_3=1792x^6\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~a}}}}\end{array}}$