00:01
We wish to find the seventh term, so n equals 7, of the binomial expansion of 7x plus 2y to the power of 15.
00:16
So since we're looking for the seventh term, the binomial coefficient is going to be 15 choose 1 less than n.
00:24
So that'll be 6.
00:25
And the reason is because our first term, we start at 0.
00:28
It'll be 15 choose 0, and then 15 choose 1 and so.
00:32
So which means the seventh term is going to be 15 to 6.
00:36
We multiply that by the first term in our binomial, which is 7x, and we take it to the power of 15 minus 6.
00:44
And now we multiply by our second term of the binomial, which is 2y, and we raise it to the power of 6.
00:52
So now we need to expand all of this.
00:55
So 15 to 6, that is 15 factorial over 6 factorial times 15 minus 6.
01:02
Six factorial, so that's nine factorial...