00:01
We have been asked to use binomial expansion to figure out the solutions to these.
00:06
So just really quickly, we're doing five questions.
00:09
We need the binomial that expands to the fifth power.
00:13
Or what is p plus q to the fifth power? so i don't know if you've learned about pascal's triangle, but there is this really cool triangle that can help you figure out the coefficients to such expansions.
00:27
And if you haven't learned pascal's triangle, i highly recommend you look it up.
00:32
But here's the fifth row, because you notice the coefficients are 1, 5, 10, 10, 5 .1.
00:38
And that is the expansion to the fifth power, because that means that this binomial here is going to have a coefficient of 1, p to the 5th, plus a coefficient of 5 times p to the 4, q to the 1 plus 10 times p to the 3.
00:58
Q to the second, plus 10 times p to the second, q to the third, plus five times p q to the fourth, plus one q to the fifth.
01:13
So that's where the coefficients come from, is this binomial theorem.
01:19
Now, we need to realize what these represent.
01:22
This means five correct...