00:02
Let's expand this binomial using all the patterns from the binomial theorem.
00:07
For example, because it's to the fourth power, we know that we can use row 4 of pascal's triangle for our coefficients.
00:13
So we can put those in place, 1, 4, 6, 4 .1.
00:18
And another pattern is the powers on a are going to descend, starting with a to the 4th, then a to the 3rd, then a to the 2nd, then a to the 1st, then a to the 0.
00:28
And the powers on 3b are going to ascend, starting with 3b to the 0, then 3b to the 1st, 3b to the 2nd, 3b to the 3b to the 3rd, and 3b to the 4th...