00:01
We wish to find a coefficient a of the term a x to the power 6 y squared of the binomial expansion 3x plus 4 y to the power of 8.
00:11
So if we're looking for the nth term of this expansion, we know the binomial coefficient is 8 to the n minus 1.
00:21
And then we multiply that by the first term, which is 3x, raised that to the power of 8 minus n minus 1, and then multiply it by the second term of the binomial, which is 4y, and that is raised the power of n minus 1.
00:35
So if we compare this and the term that we want, we can see that in order for those two to be the same, the degrees have to match.
00:43
So therefore, if we compare the degree for y, n minus 1 must be equal to 2 or n has to be equal to 3.
00:52
So this is the third term of the binomial expansion...