Question

Find the 8th term of the expansion

a.
5x3y7
b.
-14x3y7
c.
70x5y5
d.
-15x3y7


Please select the best answer from the choices provided

A
B
C
D

Answer 1

Correct choice is D

Explanation:

The i-th term of the binomial expansion
`\left((1)/(2)x-y\right)^(10)` is

`T_i=C^(10)_(i-1)\cdot \left((1)/(2)x\right)^(10+1-i)\cdot (-y)^(i-1).`

If i=8, then

`T_i=C^(10)_(7)\cdot \left((1)/(2)x\right)^(10+1-8)\cdot (-y)^(8-1)=-120\cdot \left((1)/(2)x\right)^3\cdot y^7=-120\cdot (1)/(8)x^3\cdot y^7=-15x^3y^7.`