Question

quarto termo do desenvolvimento binômio x -1 elevado a 6

Answer 1

$Um~termo~de~ordem~"p+1"~no~desenvolvimento~do~binomio\\\\(x+y)^n~\acute{e}~dado~por:\\\\\\\boxed{T_{p+1}~=~\binom{n}{p}\,.\,x^{n-p}\,.\,y^{p}}\\\\\\Observando~o~binomio~dado,~podemos~afirmar~que:\\\\\rightarrow~n~=~6\\\\\rightarrow~p+1~=~4~~~~,ou~seja,~p~=~3\\\\\rightarrow~x~=~x\\\\\rightarrow~y~=~-1\\\\\\Substituindo~os~dados~na~equacao~do~termo~geral,~temos:\\\\\\T_{4}~=~\binom{6}{3}\,.\,x^{6-3}\,.\,(-1)^{3}\\\\\\T_{4}~=~\frac{6!}{3!\,.\,(6-3)!}\,.\,x^3\,.\,(-1)$

$T_{4}~=~\frac{720}{6\,.\,6}\,.\,x^3\,.\,(-1)\\\\\\T_{4}~=~20\,.\,x^3\,.\,(-1)\\\\\\\boxed{T_{4}~=~-20x^3}$