1
00:00:00,209 --> 00:00:08,015
We are multiplying (10a - 3) by the entire polynomial (5a^2 + 7a -1).

2
00:00:08,200 --> 00:00:12,575
So to do this we can just do the distributive property. We can distribute this entire polynomial, this

3
00:00:12,575 --> 00:00:22,585
entire trinomial times each of these terms. You can have (5a^2 + 7a - 1) * 10a, and then

4
00:00:22,846 --> 00:00:26,800
(5a^2 + 7a - 1) * -3

5
00:00:26,800 --> 00:00:32,415
So let's just do that. So if we have, so let me just write it out, we could have, 5, let me write it this way :

6
00:00:32,415 --> 00:00:47,800
10a (5a^2 + 7a - 1). That's that right over here, and then we can have

7
00:00:47,800 --> 00:00:57,667
(-3 * 5a^2 + 7a - 1) , and that is this distribution right over here.

8
00:00:57,667 --> 00:01:09,467
Then we can simplify it. 10a (5a^2). 10 times 5 is fifty. a times a^2 is a^3. 10 times 7 is seventy.

9
00:01:09,467 --> 00:01:19,467
a times a is a^2; 10a * -1 is -10a. Then we distribute this -3 times all of this :

10
00:01:19,467 --> 00:01:25,067
-3 * 5a^2 is -15a^2.

11
00:01:25,067 --> 00:01:33,785
-3 * 7a is -21a; -3 * -1 is postive 3.

12
00:01:33,846 --> 00:01:41,169
And now we can try to merge like terms. This is the only a^3 term here, so this is 50a^3. I'll just rewrite it.

13
00:01:41,262 --> 00:01:49,652
Now we have two a squared terms. We have 70a^2, -15 or negative 15a^2. So we can add these two terms.

14
00:01:49,713 --> 00:01:56,200
70 of something minus 15 of that something is going to be 55 of that something.

15
00:01:56,200 --> 00:02:08,031
So +55a^2 and then we also have two a terms. We have this -10a, and then we have this -21a.

16
00:02:08,031 --> 00:02:22,823
So if we go -10 - 21 that is -31. That is -31a. So that is -31a and then we want to...

17
00:02:22,823 --> 00:02:31,367
-31a, and then finally we only have one constant term over here. We have this postive three, so +3.

18
00:02:31,517 --> 99:59:59,999
And we are done!