00:02
We're going to expand this binomial using the binomial theorem.
00:06
And the binomial theorem has a lot of patterns in it.
00:09
One of those patterns is that you can use the numbers from pascal's triangle as your coefficients.
00:14
So if we're expanding a binomial to the third power, we use row three of pascal's triangle.
00:20
So we have the numbers 1, 3, 3, and 1.
00:23
Another pattern is that the powers on x over 3 are going to descend.
00:27
So we'll start with x over 3 cubed.
00:30
Then we have x over 3 squared, then we have x over 3 to the first, then we have x over 3 to the 0, and that's just 1, so we don't write it.
00:39
And the powers on y over 2 are going to ascend, starting with y over 2 to the 0, then y over 2 to the 1st, then y over 2 to the 2 to the 2, to the 2, then y over 2 to the 3rd.
00:53
And the last pattern is that if it's a sum, you need to add all the terms...