00:01
So here we have a very complicated looking polynomial multiplied by a monomial.
00:09
What we're going to do is take our monomial and multiply it with every single term in our polynomial.
00:18
So first off, we have 5 p to 5th, q squared times negative 5 p squared q.
00:30
Then we have 5 p.
00:37
To the 5th q squared times 12 p q squared plus 5 p to the fifth q squared times negative pq plus 5p to the fifth q squared times 2q and finally plus 5 p to fifth q squared times negative 1.
01:07
And now we just have to simplify each of these.
01:10
So let's start here.
01:12
But we're going to look for first is if we can multiply any numbers together.
01:16
And we do.
01:16
We have a 5 and a negative 5.
01:18
Multiply them together and you get negative 25.
01:23
Next we're going to look for p's.
01:25
Is there any p's that we can multiply together? we have a p to the fifth.
01:30
Let's use a different fill.
01:31
We have a p to fifth and a p squared.
01:33
When you have two variables of the same base, both being p, then you add the exponent.
01:39
That gives us p to the seventh.
01:42
Finally, we're going to combine any qs...