Answer:
Correct choice is D
Step-by-step explanation:
The i-th term of the binomial expansion [tex]\left(\dfrac{1}{2}x-y\right)^{10}[/tex] is
[tex]T_i=C^{10}_{i-1}\cdot \left(\dfrac{1}{2}x\right)^{10+1-i}\cdot (-y)^{i-1}.[/tex]
If i=8, then
[tex]T_i=C^{10}_{7}\cdot \left(\dfrac{1}{2}x\right)^{10+1-8}\cdot (-y)^{8-1}=-120\cdot \left(\dfrac{1}{2}x\right)^3\cdot y^7=-120\cdot \dfrac{1}{8}x^3\cdot y^7=-15x^3y^7.[/tex]
