00:03
To expand this binomial expression, we have several patterns to follow according to the binomial theorem.
00:10
One of those patterns is that the coefficients will start out with the numbers from pascal's triangle row 4, since we have a fourth power binomial.
00:20
So let's put those coefficients in place.
00:22
We have 1, 4, 6, 4, 1.
00:28
Another pattern is that the 5m term will have descending powers starting with 5m to the 4th and then 5m cubed and then 5m squared and then 5m to the 0 which we don't write because that's just 1.
00:47
And then the 2n will have ascending powers starting with 2 into the 0, then 2 into the 1st, then 2 in to the 2nd, then 2 in to the 2nd, then 2 in to the 2nd, then 2 in to the 3rd.
01:00
And then 2n to the 4th.
01:02
I'll make a little bit more room there.
01:12
And the last pattern is that because this is a difference with a subtraction sign, we need to alternate signs.
01:19
So we get minus plus, minus, plus.
01:23
Now we need to simplify all of this...