Question

What is the sign of the second term of the expansion of (x - y)^n for n = 3, 4, and 5?

a.
positive
b.
negative


Please select the best answer from the choices provided

A
B

Answer 1

Correct choice is B

Explanation:

The i-th term of the binomial expansion
`\left(x-y\right)^(n)` is

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

For any n, when i=2,

`T_2=C^(n)_(2-1)\cdot x^(n+1-2)\cdot (-y)^(2-1)=-C^(n)_1\cdot x^(n-1)\cdot y.`

Since
`C^(n)_1` is always positive, then the second term has negative sign.