[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.00,0:00:00.50,Default,,0000,0000,0000,,
Dialogue: 0,0:00:00.50,0:00:05.12,Default,,0000,0000,0000,,We are multiplying 10a minus\N3 by the entire polynomial 5a
Dialogue: 0,0:00:05.12,0:00:07.57,Default,,0000,0000,0000,,squared plus 7a minus 1.
Dialogue: 0,0:00:07.57,0:00:09.90,Default,,0000,0000,0000,,So to do this, we can just\Ndo the distributive property.
Dialogue: 0,0:00:09.90,0:00:12.14,Default,,0000,0000,0000,,We can distribute this\Nentire polynomial,
Dialogue: 0,0:00:12.14,0:00:15.02,Default,,0000,0000,0000,,this entire trinomial,\Ntimes each of these terms.
Dialogue: 0,0:00:15.02,0:00:21.93,Default,,0000,0000,0000,,We could have 5a squared\Nplus 7a minus 1 times 10a.
Dialogue: 0,0:00:21.93,0:00:26.21,Default,,0000,0000,0000,,And then 5a squared plus 7a\Nminus 1 times negative 3.
Dialogue: 0,0:00:26.21,0:00:27.89,Default,,0000,0000,0000,,So let's just do that.
Dialogue: 0,0:00:27.89,0:00:31.32,Default,,0000,0000,0000,,So if we have-- so let\Nme just write it out.
Dialogue: 0,0:00:31.32,0:00:32.36,Default,,0000,0000,0000,,Let me write it this way.
Dialogue: 0,0:00:32.36,0:00:43.90,Default,,0000,0000,0000,,10a times 5a squared\Nplus 7a minus 1.
Dialogue: 0,0:00:43.90,0:00:46.42,Default,,0000,0000,0000,,That's that right over here.
Dialogue: 0,0:00:46.42,0:00:52.18,Default,,0000,0000,0000,,And then we can have\Nminus 3 times 5a squared
Dialogue: 0,0:00:52.18,0:00:54.71,Default,,0000,0000,0000,,plus 7a minus 1.
Dialogue: 0,0:00:54.71,0:00:57.19,Default,,0000,0000,0000,,And that is this\Ndistribution right over here.
Dialogue: 0,0:00:57.19,0:00:58.80,Default,,0000,0000,0000,,And then we can simplify it.
Dialogue: 0,0:00:58.80,0:01:03.41,Default,,0000,0000,0000,,10a times 5a squared--\N10 times 5 is 50.
Dialogue: 0,0:01:03.41,0:01:06.36,Default,,0000,0000,0000,,a times a squared\Nis a to the third.
Dialogue: 0,0:01:06.36,0:01:09.82,Default,,0000,0000,0000,,10 times 7 is 70.
Dialogue: 0,0:01:09.82,0:01:12.16,Default,,0000,0000,0000,,a times a is a squared.
Dialogue: 0,0:01:12.16,0:01:16.33,Default,,0000,0000,0000,,10a times negative\N1 is negative 10a.
Dialogue: 0,0:01:16.33,0:01:19.07,Default,,0000,0000,0000,,Then we distribute this\Nnegative 3 times all of this.
Dialogue: 0,0:01:19.07,0:01:24.90,Default,,0000,0000,0000,,Negative 3 times 5a squared\Nis negative 15a squared.
Dialogue: 0,0:01:24.90,0:01:29.28,Default,,0000,0000,0000,,Negative 3 times\N7a is negative 21a.
Dialogue: 0,0:01:29.28,0:01:33.38,Default,,0000,0000,0000,,Negative 3 times\Nnegative 1 is positive 3.
Dialogue: 0,0:01:33.38,0:01:35.95,Default,,0000,0000,0000,,And now we can try\Nto merge like terms.
Dialogue: 0,0:01:35.95,0:01:38.33,Default,,0000,0000,0000,,This is the only a to\Nthe third term here.
Dialogue: 0,0:01:38.33,0:01:39.63,Default,,0000,0000,0000,,So this is 50a to the third.
Dialogue: 0,0:01:39.63,0:01:41.34,Default,,0000,0000,0000,,I'll just rewrite it.
Dialogue: 0,0:01:41.34,0:01:43.66,Default,,0000,0000,0000,,Now we have two a squared terms.
Dialogue: 0,0:01:43.66,0:01:47.81,Default,,0000,0000,0000,,We have 70a squared minus\N15, or negative 15a squared.
Dialogue: 0,0:01:47.81,0:01:49.88,Default,,0000,0000,0000,,So we can add these two terms.
Dialogue: 0,0:01:49.88,0:01:53.19,Default,,0000,0000,0000,,70 of something minus\N15 of that something
Dialogue: 0,0:01:53.19,0:01:56.95,Default,,0000,0000,0000,,is going to be 55\Nof that something.
Dialogue: 0,0:01:56.95,0:02:01.49,Default,,0000,0000,0000,,So plus 55a squared.
Dialogue: 0,0:02:01.49,0:02:03.80,Default,,0000,0000,0000,,And then we also\Nhave two a terms.
Dialogue: 0,0:02:03.80,0:02:07.52,Default,,0000,0000,0000,,We have this negative 10a, and\Nthen we have this negative 21a.
Dialogue: 0,0:02:07.52,0:02:12.43,Default,,0000,0000,0000,,So if we go negative 10 minus\N21, that is negative 31.
Dialogue: 0,0:02:12.43,0:02:14.17,Default,,0000,0000,0000,,That is negative 31a.
Dialogue: 0,0:02:14.17,0:02:23.67,Default,,0000,0000,0000,,
Dialogue: 0,0:02:23.67,0:02:27.29,Default,,0000,0000,0000,,And then finally, we only have\None constant term over here.
Dialogue: 0,0:02:27.29,0:02:29.52,Default,,0000,0000,0000,,We have this positive 3.
Dialogue: 0,0:02:29.52,0:02:31.61,Default,,0000,0000,0000,,So plus 3.
Dialogue: 0,0:02:31.61,0:02:34.27,Default,,0000,0000,0000,,And we are done.