00:01
Well, what is the binomial theorem to write out the expansion square root of x plus 5 to the power of 3? so here's the binomial theorem, and i've put a pascal's triangle here so that we can easily find those coefficients without punching it into a calculator.
00:20
So if we're taking into the power of 3, then that means we're using this row here.
00:25
So the binomial coefficients are 1 -3 -1.
00:28
So let's go ahead and write those down.
00:31
Three, three, one.
00:34
Next, we just have to follow the binomial theorem.
00:37
So we start with the first term of the binomial to the power of n, and that the power will decrease by one after that.
00:43
So the first term in our binomial is square root x.
00:47
So we'll raise that to the power of three, and then the next term it'll be to the power of two, and then it'll be to the power of one, and the last one will be to the power of zero, which is just one.
00:58
Next, the second term of the binomial, we start by raising into the power of two, or 0, which is just 1, so you don't see it.
01:04
And the power will increase by 1 after that...