If x is an odd integer and y is an odd integer then xy is an odd integer. Use direct proof to prove the following.
I am stumped on where to go from here. All I know is that the definition of an odd integer is n=2k+1 where n is the integer.
So I assume that I need x=2n+1 and y=2m+1 but I really don't know where to go from here. This seems really simple but where to start is stubborn to me.
Is it university level ?
read this : FOIL rule - Wikipedia, the free encyclopedia
ok so ive been working on this..
x= 2n+1 y=2m+1
xy= (2n+1)(2m)+1
xy= 4nm +2n +2m +1 using FOIL
2(nm+n+m) +1 using factoring by 2
n & m are real numbers so...
nm + n + m = k (real number) using addition/multiplication of real numbers
2k+1 is the same as the definition of odd number...
is this right? Can anyone add to this.