Alg10.9

Find the fifth term in the expansion of $(2x+\frac{1}{3y})^8\,$

The fifth term in the expansion is $T_5=T_{4+1}=8\!C_4\cdot (2x)^{8-4}\cdot (\frac{1}{3y})^4\,$

$T_5=8\!C_4 \cdot 2^4 \cdot x^4\cdot \frac{1}{81y^4}=8\!C_4 \cdot [\frac{16x^4}{81y^4}]\,$