00:01
Okay, so we want to prove that the cube of any odd number is always an odd number.
00:04
So i'm going to represent an odd number as 2n plus 1.
00:08
The reason why is, no matter what n is, it could be any integer i want.
00:13
Well, if we stick with a whole positonar, so let's make it any natural number, or any, sorry, any whole number.
00:20
So you're 0, 2 times 0 is 0 plus 1 is 1, that's an odd number.
00:24
2 times 1 is 2 plus 1 is 3.
00:27
That's the next odd number.
00:28
So these can be odd numbers.
00:29
So any odd number can be represented as 2n plus 1.
00:33
So the cube of that will look like this.
00:37
So i'm going to start with taking 2n plus 1 times 2n plus 1 here.
00:42
But then i'll also multiply by another one here.
00:44
So let's distribute here first.
00:46
So that's going to give me 4n squared...