00:03
All right.
00:04
We are asked to the direction say factorize this.
00:07
I imagine it means like try and separate this into individual parts, individual factors here.
00:13
So the first thing we want to notice is that this is really just a complicated difference of two squares.
00:19
X minus two to the eighth is a perfect square and 256 is also a perfect square.
00:25
So what we can do is think about that difference of two squares.
00:29
We're going to use that a couple of times here.
00:30
So just to make sure you understand what we're doing here, you know, i'm just going with the x squared minus 4.
00:37
We should know that that factors into the square root minus the square root, so x minus 2 times the square root plus the square root.
00:44
All right.
00:45
So that's the same thing i'm going to do here.
00:47
It just looks a little bit worse.
00:49
So what times itself is equal to x minus 2 to the 8th? well, that would be x minus 2 to the fourth, right? if we take the square root of this, we'd raise it to the one -half power, so we just get it to the fourth.
01:00
So that's my first thing.
01:02
I'm going to make it x minus 2 to the fourth minus and the square root of 256 is 16.
01:09
All right.
01:09
I'll use brackets, the squared ones for this, just to kind of show the difference between my factors.
01:13
So it's the square root minus the square root times and then the square root x minus 2.
01:20
Let me raise that one here.
01:23
X minus 2 to the fourth and then plus the square root.
01:27
So plus 16.
01:30
All right.
01:32
All right.
01:33
Now, i wish i had written it in the other order.
01:35
I'm just going to change it.
01:36
I'm going to change the order here and make this one the plus and this one the minus.
01:40
Because the plus, i'm not really going to do anything else with that.
01:42
I mean, in the end, maybe your teacher would want you to multiply this out, but that's, you know, we can get to that and do it at the end if we want.
01:51
What i want to make sure that you see is that this is another difference of two squares now.
01:55
The plus cancels that out.
01:57
We don't have a sum of two.
01:59
Squares formula, not an easy one like that.
02:01
So the difference of two squares, the ones we can do that trick with.
02:04
So let's do that process again.
02:06
So now i'm going to do the difference of two squares on this.
02:10
So the square root of x minus two to the fourth is x minus two squared.
02:15
And i'll put the plus first this time.
02:17
So plus four...