Question

No desenvolvimento de (2x + y)
5
, com expoentes decrescentes de x, determine o quarto termo.

Answer 1

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

$\Large\boxed{\begin{array}{l}\sf (2x+y)^5\begin{cases}\sf a=2x\\\sf b=y\\\sf n=5\end{cases}\\\sf p+1=4\\\sf p=4-1\\\sf p=3\\\sf T_{3+1}=\displaystyle\sf\binom{5}{3}~(2x)^{5-3}\cdot y^3\\\sf T_{4}=10\cdot(2x)^2\cdot y^3\\\sf T_{4}=40x^2y^3\end{array}}$