0:00:00.500,0:00:05.120
We are multiplying 10a minus[br]3 by the entire polynomial 5a

0:00:05.120,0:00:07.567
squared plus 7a minus 1.

0:00:07.567,0:00:09.900
So to do this, we can just[br]do the distributive property.

0:00:09.900,0:00:12.140
We can distribute this[br]entire polynomial,

0:00:12.140,0:00:15.020
this entire trinomial,[br]times each of these terms.

0:00:15.020,0:00:21.930
We could have 5a squared[br]plus 7a minus 1 times 10a.

0:00:21.930,0:00:26.210
And then 5a squared plus 7a[br]minus 1 times negative 3.

0:00:26.210,0:00:27.890
So let's just do that.

0:00:27.890,0:00:31.319
So if we have-- so let[br]me just write it out.

0:00:31.319,0:00:32.360
Let me write it this way.

0:00:32.360,0:00:43.900
10a times 5a squared[br]plus 7a minus 1.

0:00:43.900,0:00:46.420
That's that right over here.

0:00:46.420,0:00:52.180
And then we can have[br]minus 3 times 5a squared

0:00:52.180,0:00:54.710
plus 7a minus 1.

0:00:54.710,0:00:57.190
And that is this[br]distribution right over here.

0:00:57.190,0:00:58.800
And then we can simplify it.

0:00:58.800,0:01:03.410
10a times 5a squared--[br]10 times 5 is 50.

0:01:03.410,0:01:06.360
a times a squared[br]is a to the third.

0:01:06.360,0:01:09.820
10 times 7 is 70.

0:01:09.820,0:01:12.160
a times a is a squared.

0:01:12.160,0:01:16.330
10a times negative[br]1 is negative 10a.

0:01:16.330,0:01:19.070
Then we distribute this[br]negative 3 times all of this.

0:01:19.070,0:01:24.900
Negative 3 times 5a squared[br]is negative 15a squared.

0:01:24.900,0:01:29.280
Negative 3 times[br]7a is negative 21a.

0:01:29.280,0:01:33.380
Negative 3 times[br]negative 1 is positive 3.

0:01:33.380,0:01:35.950
And now we can try[br]to merge like terms.

0:01:35.950,0:01:38.330
This is the only a to[br]the third term here.

0:01:38.330,0:01:39.630
So this is 50a to the third.

0:01:39.630,0:01:41.340
I'll just rewrite it.

0:01:41.340,0:01:43.660
Now we have two a squared terms.

0:01:43.660,0:01:47.810
We have 70a squared minus[br]15, or negative 15a squared.

0:01:47.810,0:01:49.880
So we can add these two terms.

0:01:49.880,0:01:53.190
70 of something minus[br]15 of that something

0:01:53.190,0:01:56.950
is going to be 55[br]of that something.

0:01:56.950,0:02:01.490
So plus 55a squared.

0:02:01.490,0:02:03.800
And then we also[br]have two a terms.

0:02:03.800,0:02:07.520
We have this negative 10a, and[br]then we have this negative 21a.

0:02:07.520,0:02:12.430
So if we go negative 10 minus[br]21, that is negative 31.

0:02:12.430,0:02:14.170
That is negative 31a.

0:02:23.670,0:02:27.290
And then finally, we only have[br]one constant term over here.

0:02:27.290,0:02:29.520
We have this positive 3.

0:02:29.520,0:02:31.610
So plus 3.

0:02:31.610,0:02:34.270
And we are done.