Question

Calcule o 7° termo no desenvolvimento de (a-3x2)9

Answer 1

$(a-3x^2)^9\Longrightarrow(-3x^2+a)^9\\\\\\\\p+1=7\longrightarrow{p}=6\\\\\\\text{Termo geral de }(x+a)^n:\\\\T_{p+1}=\displaystyle\binom{n}{p}x^{n-p}\cdot{a}^p\\\\\\\text{Substituindo os valores dados, temos:}\\\\T_{p+1}=\displaystyle\binom{n}{p}x^{n-p}\cdot{a}^p\\\\\\T_{6+1}=\displaystyle\binom{9}{6}(-3x^2)^{9-6}\cdot{a}^6\\\\\\T_{7}=\dfrac{9!}{6!(9-6)!}\cdot(-3x^2)^3\cdot{a}^6\\\\\\T_{7}=\dfrac{9!}{6!3!}\cdot{(-3)}^3\cdot(x^2)^3\cdot{a}^6\\\\\\T_{7}=\dfrac{9\times8\times7}{6}\cdot-27x^6a^6\\\\\\T_{7}=84\cdot-27x^6a^6\\\\\boxed{T_{7}=-2268x^6a^6}$