00:01
If we want to expand the binomial expression, 3x plus 1 to the 4th, we need to use the binomial theorem to the right.
00:13
So from this binomial, we could see that x equals 3x.
00:21
And when i say x, i mean x over here.
00:25
A equals 1, and the n over here, which is the exponent, equals 4.
00:33
So we can use this theorem to expand the binomial.
00:35
The first term, n equals 4, j equals 0.
00:41
So we have 4 to 0 times x, which is really 3x to the 4th because 4 minus 0 is 4 times a, which in this case is 1, to the j, which is 0.
01:07
With a second term, j equals 1.
01:10
So we get 4 choose 1 times 3x to the 3rd.
01:18
Times 1 to the 1.
01:23
For the third term, j equals 2.
01:24
So we get 4, choose 2, times 3x to the second, times 1 to the second.
01:36
For the next term, j equals 3, so we get 4 choose 3 times 3x to the 4 minus 3, so it's 3x to the 1st, times 1 to the 3.
01:55
And the last term, j equals 4.
01:58
So it would be 4 choose 4 times 3x to the 0 times 1 to the 4th...