Question

o terceiro termo no desenvolvimento do binômio (x+3)elevado a 5 na fórmula,tp+1=(n/p).(x)n-p.(a)p

Answer 1

--> a = 3

--> n = 5

Como estamos interessados no 3° termo, temos:

$p+1~=~3\\\\\\p~=~3-1\\\\\\\boxed{p~=~2}$

Agora, utilizando a equação do termo geral, temos:

$T_{p+1}~=~\displaystyle\binom{n}{p}~.~x^{n-p}~.~a^{p}\\\\\\Substituindo~os~valores:\\\\\\T_3~=~\displaystyle\binom{5}{2}~.~x^{5-2}~.~3^{2}\\\\\\T_3~=~\dfrac{5!}{2!\,.\,(5-2)!}~.~x^3~.~9\\\\\\T_3~=~\dfrac{5~.~4~.~3!}{2~.~3!}~.~x^3~.~9\\\\\\T_3~=~\dfrac{20}{2}~.~x^3~.~9\\\\\\\boxed{T_3~=~90x^3}$