Question

Qual é o coeficiente do 3°termo do binômio u+t (6)

Answer 1

$T_{p+1}=\binom{n}{p}a^{n-p}b^{p}\\\\ (u+t)^6\ \to\ n=6;\ p+1=3\ \to\ p=2\\\\ T_{2+1}=\binom{6}{2}u^{6-2}t^{2}\ \to\ T_3=\dfrac{6!}{4!*2!}u^4t^2=\dfrac{6*5}{2}u^4t^2=\boxed{15u^4t^2}\\\\ \mathrm{Coeficiente}=15$