Question

O binômio (x³+ 1/y²)^25, escreva o termo x^9

Answer 1

$T_{p+1} = {n \choose p}\cdot a^{n-p}\cdot b^p$

$T_{p+1} = {25 \choose p}\cdot \left(x^3\right)^{25-p}\cdot \left(\dfrac{1}{y^2}\right)^p$

$T_{p+1} = {25 \choose p}\cdot x^{75-3p}\cdot y^{-2p}$

$75-3p = 9 \\~\\25-p = 3 \\~\\p = 22$

$T_{22+1} = {25 \choose 22}\cdot x^{75-3\cdot22}\cdot y^{-2\cdot22}$

$T_{23} = {25 \choose 22}\cdot x^{9}\cdot y^{-44}$

$T_{23} = {25 \choose 3}\cdot x^{9}\cdot y^{-44}$

$T_{23} =\dfrac{25\cdot24\cdot23}{3\cdot2}\cdot x^{9}\cdot y^{-44}$

$T_{23} =\dfrac{2300\cdot x^{9}}{y^{44}}$