00:01
So in this problem, we're going to be using pascal's triangle to write the binomial expansions.
00:08
So with this binomial expansion problem, we work with a plus b, and this is an a minus b form.
00:16
So it's best to write it as an addition inside.
00:19
So we'll just start with that.
00:20
So now we have x plus minus y, whole squared, whole fifth.
00:26
So when we look at these binomial expansion problems, the n in the binomial expansion is equal to 5.
00:34
So that's where we're going to kind of start at.
00:37
And once we have this n, we have to look to the row that has, you have to look to the row of pascal's triangle that has five as the second term, and that's this line.
00:48
And what this tells us is that there's going to be six terms in this binomial expansion.
00:54
So when we do it, we start, we start at a to the nth times b to the 0th, and then we go down one for each term a, and then we go up one for each term b.
01:09
So i'll write in the next line what we should have with slots for the coefficients.
01:15
So here's a slot, and since we're starting at a to the nth, we start at a to the 5th.
01:21
And b is technically to the 0th.
01:24
Let me write it as our actual a term, so that's a little bit less confusing.
01:29
It's x to the fifth, and b, which is minus y, is to the 0th, so we can kind of ignore it...