Question

Which statements are true?
(look at picture)​

Answer 1

D is true, E is true, F is true

Explanation:

Hello,

n is an odd number it means that n = 2a+1 where a is integer

A

`n^2-1=(2a+1)^2-1=4a^2+4a+1-1=4a(a+1)`

this is not an odd number

B

`n(n-1)=(2a+1)2a`

this is not an odd number

C

`(n-1)^2=(2a+1-1)^2=4a^2`

this is not an odd number

D

`n^2+2=(2a+1)^2+2=4a^2+4a+1+2=4a^2+4a+3= 2(2a^2+2a+1)+1`

so this is an odd number

E

`n(n-2)=(2a+1)(2a-1)=4a^2-1=4a^2-2+1=2(2a^2-1)+1`

so this is an odd number

F

`(n-2)^2=(2a+1-2)^2=(2a-1)^2=4a^2-4a+1 = 2(2a^2-2a)+1`

this is an odd number

hope this helps