00:01
Here we have the quantity x plus 1 raised to the 8th power, and we can expand this out to have something that looks like x to the 8th power times its coefficient plus x to 7th power times its coefficient and so on.
00:20
And if we want to solve this, we can expand this out this way and see what the coefficients are.
00:28
Or if we want, we can just find the coefficients of the terms and do it that way.
00:37
So if we want to find the coefficient of x to the 6th power, for example, we can use the binomial coefficient theorem in our section.
00:48
So here, a equals x, b equals 1, and n equals 8.
00:54
And to find the coefficient of a to the n minus r times b to the r, we solve this, so n choose r, which is equal to n factorial over n minus r factorial times r factorial...