bm42400
contestada

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

Respuesta :

frika

Answer:

Correct choice is B

Step-by-step explanation:

The i-th term of the binomial expansion [tex]\left(x-y\right)^{n}[/tex] is

[tex]T_i=C^{n}_{i-1}\cdot \left(x\right)^{n+1-i}\cdot (-y)^{i-1}.[/tex]

For any n, when i=2,

[tex]T_2=C^{n}_{2-1}\cdot x^{n+1-2}\cdot (-y)^{2-1}=-C^{n}_1\cdot x^{n-1}\cdot y.[/tex]

Since [tex]C^{n}_1[/tex] is always positive, then the second term has negative sign.