00:01
Okay, i want to find the sixth term in this expansion.
00:09
Well, some rough work over here just to show you what's going on.
00:14
The first term will be x power 8.
00:18
Next term will contain x7.
00:21
Next term x6.
00:23
So the x powers decrease all the time.
00:26
And that's four of them.
00:31
So one, two, three, four, five, six.
00:35
So this term is what i want.
00:38
It contains the x -cube term.
00:42
So to do that then, i don't expand the whole thing out.
00:46
There's no need.
00:47
I know what i'm going to have basically three brackets like this.
00:53
First will be the number in front of the x, y term, as the coefficient from pascal's triangle or from the binomial theorem.
01:05
And here will be x, we'll be the number.
01:08
2y here will be 8 so that's automatic the 8 from the power here x and 2y i want 3 here which means here must be 5 is 3 here here is 3 so that's the actual term which i now have to work out 1 8 3 means 8 c 3 which is 8 factorial over 5 factorial 3 factorial.
01:45
So i have 8 times 7 times 6.
01:49
That will be this divided by this over 6.
01:56
3 factorial, 3 times 2 times 1.
01:59
That goes away.
02:01
So i'm left with 56.
02:04
Or just use the calculator, the ncr button on the ti 84 plus.
02:10
You press math, go to prob.
02:14
Third one down is ncr.
02:16
Type it in.
02:16
You get the answer a bit faster.
02:20
So it's 56 then here, x cubed, and 2 power 5 is 32, y, 5.
02:30
So 56 times 32 is 8192, x cubed, y, power 5, and that's the answer...