[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.26,0:00:02.65,Default,,0000,0000,0000,,- [Voiceover] Alright, in this video,
Dialogue: 0,0:00:02.65,0:00:06.48,Default,,0000,0000,0000,,we're gonna be multiplying\Nmonomials together.
Dialogue: 0,0:00:08.19,0:00:12.08,Default,,0000,0000,0000,,Let me give you an example of a monomial.
Dialogue: 0,0:00:12.08,0:00:14.58,Default,,0000,0000,0000,,4x squared, that's a monomial.
Dialogue: 0,0:00:15.70,0:00:17.36,Default,,0000,0000,0000,,Now, why?
Dialogue: 0,0:00:17.36,0:00:21.53,Default,,0000,0000,0000,,Well, mono means one, which\Nrefers to the number of terms.
Dialogue: 0,0:00:24.89,0:00:28.16,Default,,0000,0000,0000,,So this 4x squared, this is all one term.
Dialogue: 0,0:00:28.16,0:00:30.69,Default,,0000,0000,0000,,So we're gonna be working\Nwith things like that.
Dialogue: 0,0:00:30.69,0:00:33.29,Default,,0000,0000,0000,,What won't we be working with?
Dialogue: 0,0:00:33.29,0:00:36.21,Default,,0000,0000,0000,,Well what about 4x squared plus 5x.
Dialogue: 0,0:00:37.17,0:00:38.98,Default,,0000,0000,0000,,How many terms are there?
Dialogue: 0,0:00:38.98,0:00:41.49,Default,,0000,0000,0000,,4x squared's the first\Nterm, 5x is the second term,
Dialogue: 0,0:00:41.49,0:00:43.66,Default,,0000,0000,0000,,so this is not a monomial,
Dialogue: 0,0:00:44.54,0:00:48.70,Default,,0000,0000,0000,,this is actually called a\Nbinomial, because bi means two.
Dialogue: 0,0:00:50.50,0:00:54.18,Default,,0000,0000,0000,,Like your bicycle's got\Ntwo wheels, for example.
Dialogue: 0,0:00:54.18,0:00:56.08,Default,,0000,0000,0000,,So not yet, go on to the future videos
Dialogue: 0,0:00:56.08,0:00:57.38,Default,,0000,0000,0000,,if you're ready for binomials.
Dialogue: 0,0:00:57.38,0:00:58.55,Default,,0000,0000,0000,,But we're just gonna be working
Dialogue: 0,0:00:58.55,0:01:00.80,Default,,0000,0000,0000,,with multiplying monomials together.
Dialogue: 0,0:01:00.80,0:01:03.89,Default,,0000,0000,0000,,So can we grab an example to look at.
Dialogue: 0,0:01:06.46,0:01:10.03,Default,,0000,0000,0000,,By the end of this video,\Nit should be very easy
Dialogue: 0,0:01:10.03,0:01:13.87,Default,,0000,0000,0000,,for you to multiply this\Nmonomial, 5x squared,
Dialogue: 0,0:01:15.93,0:01:18.14,Default,,0000,0000,0000,,by this monomial.
Dialogue: 0,0:01:18.14,0:01:21.33,Default,,0000,0000,0000,,And I'm actually just gonna\Ngive you the answer right here.
Dialogue: 0,0:01:21.33,0:01:22.97,Default,,0000,0000,0000,,And then I'm gonna slowly\Nwalk you through some other
Dialogue: 0,0:01:22.97,0:01:25.27,Default,,0000,0000,0000,,questions that will lead us to why.
Dialogue: 0,0:01:25.27,0:01:28.94,Default,,0000,0000,0000,,But the answer to this\Nis 20x to the eighth.
Dialogue: 0,0:01:31.98,0:01:33.38,Default,,0000,0000,0000,,20x to the eighth.
Dialogue: 0,0:01:33.38,0:01:35.39,Default,,0000,0000,0000,,Take a look at that, see if\Nyou can notice a pattern.
Dialogue: 0,0:01:35.39,0:01:37.78,Default,,0000,0000,0000,,What did we do with the five\Nand the four to get the 20?
Dialogue: 0,0:01:37.78,0:01:40.78,Default,,0000,0000,0000,,What did we do with the two\Nand the six to get the eight?
Dialogue: 0,0:01:40.78,0:01:43.47,Default,,0000,0000,0000,,That's getting a little\Nahead of ourselves though.
Dialogue: 0,0:01:43.47,0:01:44.90,Default,,0000,0000,0000,,Before we can dive in there,
Dialogue: 0,0:01:44.90,0:01:48.09,Default,,0000,0000,0000,,let's remember some of\Nthe exponent properties.
Dialogue: 0,0:01:48.09,0:01:49.39,Default,,0000,0000,0000,,A very specific exponent property
Dialogue: 0,0:01:49.39,0:01:51.72,Default,,0000,0000,0000,,that you should've seen before.
Dialogue: 0,0:01:51.72,0:01:55.28,Default,,0000,0000,0000,,If we look at five squared\Ntimes five to the fourth power,
Dialogue: 0,0:01:55.28,0:01:57.24,Default,,0000,0000,0000,,what's that going to equal?
Dialogue: 0,0:01:57.24,0:01:59.81,Default,,0000,0000,0000,,Well, if you remember\Nyour exponent property,
Dialogue: 0,0:01:59.81,0:02:03.80,Default,,0000,0000,0000,,we'll do a quick reminder\Nhere, I always add my exponent.
Dialogue: 0,0:02:03.80,0:02:06.07,Default,,0000,0000,0000,,So five squared times\Nfive to the fourth power
Dialogue: 0,0:02:06.07,0:02:08.73,Default,,0000,0000,0000,,is equal to five to the sixth power.
Dialogue: 0,0:02:08.73,0:02:10.55,Default,,0000,0000,0000,,What about three to the fourth power
Dialogue: 0,0:02:10.55,0:02:13.64,Default,,0000,0000,0000,,times three to the fifth power?
Dialogue: 0,0:02:13.64,0:02:16.75,Default,,0000,0000,0000,,Well, again, I always add my exponents.
Dialogue: 0,0:02:16.75,0:02:20.05,Default,,0000,0000,0000,,Four plus five is three\Nto the ninth power,
Dialogue: 0,0:02:20.05,0:02:23.60,Default,,0000,0000,0000,,and my base of three stays the same.
Dialogue: 0,0:02:23.60,0:02:25.56,Default,,0000,0000,0000,,Great, so if you remember that,
Dialogue: 0,0:02:25.56,0:02:27.32,Default,,0000,0000,0000,,now we're ready to really start
Dialogue: 0,0:02:27.32,0:02:29.65,Default,,0000,0000,0000,,multiplying monomials that are new to you.
Dialogue: 0,0:02:29.65,0:02:31.40,Default,,0000,0000,0000,,And the new thing there\Nis that we are going
Dialogue: 0,0:02:31.40,0:02:33.80,Default,,0000,0000,0000,,to have variables involved.
Dialogue: 0,0:02:33.80,0:02:37.97,Default,,0000,0000,0000,,So let's start, let's take a\Nlook at two monomials here.
Dialogue: 0,0:02:39.46,0:02:44.22,Default,,0000,0000,0000,,The first monomial is 4x,\Nand the second one is just x.
Dialogue: 0,0:02:44.22,0:02:47.82,Default,,0000,0000,0000,,And the four, I don't have\Nanother number to multiply by,
Dialogue: 0,0:02:47.82,0:02:48.84,Default,,0000,0000,0000,,just got the four.
Dialogue: 0,0:02:48.84,0:02:51.34,Default,,0000,0000,0000,,And can I simplify x times x?
Dialogue: 0,0:02:51.34,0:02:54.25,Default,,0000,0000,0000,,Well, that's equal to x squared.
Dialogue: 0,0:02:55.39,0:02:56.70,Default,,0000,0000,0000,,Remember if I just have a variable,
Dialogue: 0,0:02:56.70,0:02:59.74,Default,,0000,0000,0000,,and there's no exponent there,
Dialogue: 0,0:02:59.74,0:03:01.56,Default,,0000,0000,0000,,it's equivalent to having a one,
Dialogue: 0,0:03:01.56,0:03:04.61,Default,,0000,0000,0000,,so x to the first power\Ntimes x to the first power,
Dialogue: 0,0:03:04.61,0:03:07.25,Default,,0000,0000,0000,,I add my exponents like\Nwe just talked about,
Dialogue: 0,0:03:07.25,0:03:09.63,Default,,0000,0000,0000,,and one plus one is equal to two.
Dialogue: 0,0:03:09.63,0:03:13.30,Default,,0000,0000,0000,,Great, so let's move\Non to another one here.
Dialogue: 0,0:03:15.24,0:03:17.07,Default,,0000,0000,0000,,If I have 4t times 3t.
Dialogue: 0,0:03:19.06,0:03:22.99,Default,,0000,0000,0000,,Well, four times three\Nis gonna be equal to 12,
Dialogue: 0,0:03:22.99,0:03:26.49,Default,,0000,0000,0000,,so I've combined my coefficients.
Dialogue: 0,0:03:26.49,0:03:30.69,Default,,0000,0000,0000,,And then t times t, again,\Nthink of a one being there,
Dialogue: 0,0:03:30.69,0:03:32.77,Default,,0000,0000,0000,,is going to be t squared.
Dialogue: 0,0:03:35.59,0:03:38.03,Default,,0000,0000,0000,,So the answer here is 12t squared.
Dialogue: 0,0:03:38.03,0:03:40.23,Default,,0000,0000,0000,,So let's keep going,
Dialogue: 0,0:03:40.23,0:03:42.14,Default,,0000,0000,0000,,and once you get into the rhythm of these,
Dialogue: 0,0:03:42.14,0:03:44.20,Default,,0000,0000,0000,,they become pretty alright.
Dialogue: 0,0:03:44.20,0:03:48.20,Default,,0000,0000,0000,,So what if I had 4p to\Nthe fifth power times,
Dialogue: 0,0:03:48.20,0:03:50.87,Default,,0000,0000,0000,,let's say 5p to the third power.
Dialogue: 0,0:03:52.46,0:03:54.27,Default,,0000,0000,0000,,What would that equal?
Dialogue: 0,0:03:54.27,0:03:56.30,Default,,0000,0000,0000,,Well you're gonna notice a pattern here
Dialogue: 0,0:03:56.30,0:03:57.56,Default,,0000,0000,0000,,that we've been pickin' up on,
Dialogue: 0,0:03:57.56,0:04:00.64,Default,,0000,0000,0000,,which is that I'm always gonna\Nmultiply my coefficients,
Dialogue: 0,0:04:00.64,0:04:04.06,Default,,0000,0000,0000,,so four times five, is going to equal 20.
Dialogue: 0,0:04:05.74,0:04:09.16,Default,,0000,0000,0000,,And I'm always going to add my exponents.
Dialogue: 0,0:04:09.16,0:04:12.16,Default,,0000,0000,0000,,So p to the fifth and p to the third
Dialogue: 0,0:04:14.65,0:04:16.73,Default,,0000,0000,0000,,is p to the eighth power.
Dialogue: 0,0:04:18.97,0:04:21.76,Default,,0000,0000,0000,,so I multiply four and five til we get 20,
Dialogue: 0,0:04:21.76,0:04:25.26,Default,,0000,0000,0000,,I add five and three to get eight.
Dialogue: 0,0:04:25.26,0:04:27.03,Default,,0000,0000,0000,,And if you really wanted\Nto see why that is,
Dialogue: 0,0:04:27.03,0:04:28.87,Default,,0000,0000,0000,,let's really dive in\Nhere and let's break down
Dialogue: 0,0:04:28.87,0:04:31.82,Default,,0000,0000,0000,,this first term, let's\Nbreak down 4p to the fifth.
Dialogue: 0,0:04:31.82,0:04:33.89,Default,,0000,0000,0000,,I can write that out as four times p,
Dialogue: 0,0:04:33.89,0:04:38.06,Default,,0000,0000,0000,,times p, times p, times p,\Ntimes p, that's five of 'em.
Dialogue: 0,0:04:39.46,0:04:40.74,Default,,0000,0000,0000,,That's four and five p's.
Dialogue: 0,0:04:40.74,0:04:42.68,Default,,0000,0000,0000,,And then that second term I can write as
Dialogue: 0,0:04:42.68,0:04:45.77,Default,,0000,0000,0000,,times five times p, times p, times p.
Dialogue: 0,0:04:47.15,0:04:50.70,Default,,0000,0000,0000,,What I'm gonna do is I'm\Ngonna group my numbers,
Dialogue: 0,0:04:50.70,0:04:52.14,Default,,0000,0000,0000,,cause I can work with numbers together,
Dialogue: 0,0:04:52.14,0:04:55.48,Default,,0000,0000,0000,,so let's put four times\Nfive at the very front,
Dialogue: 0,0:04:55.48,0:04:58.96,Default,,0000,0000,0000,,and then it just becomes a\Nmatter of how many p's do I have?
Dialogue: 0,0:04:58.96,0:05:01.39,Default,,0000,0000,0000,,We'll put all of those together as well.
Dialogue: 0,0:05:01.39,0:05:05.14,Default,,0000,0000,0000,,So I had five p's, so\Nthere's the first five,
Dialogue: 0,0:05:06.11,0:05:08.16,Default,,0000,0000,0000,,and then I had three more.
Dialogue: 0,0:05:08.16,0:05:11.53,Default,,0000,0000,0000,,And we can simplify this\Ncrazy looking expression
Dialogue: 0,0:05:11.53,0:05:14.85,Default,,0000,0000,0000,,by just multiplying my four\Nand my five to be my 20,
Dialogue: 0,0:05:14.85,0:05:18.44,Default,,0000,0000,0000,,and then writing this with an exponent,
Dialogue: 0,0:05:18.44,0:05:20.51,Default,,0000,0000,0000,,that's the beauty of exponents,\Nthat's why we have 'em,
Dialogue: 0,0:05:20.51,0:05:23.47,Default,,0000,0000,0000,,is we can write a crazy\Nexpression like that
Dialogue: 0,0:05:23.47,0:05:24.68,Default,,0000,0000,0000,,as p to the eighth,
Dialogue: 0,0:05:24.68,0:05:26.91,Default,,0000,0000,0000,,and you'll notice that this is, of course,
Dialogue: 0,0:05:26.91,0:05:29.59,Default,,0000,0000,0000,,what we got the first time.
Dialogue: 0,0:05:29.59,0:05:30.43,Default,,0000,0000,0000,,So great.
Dialogue: 0,0:05:34.71,0:05:36.98,Default,,0000,0000,0000,,What about 5y to the sixth times
Dialogue: 0,0:05:36.98,0:05:39.65,Default,,0000,0000,0000,,negative 3y to the eighth power?
Dialogue: 0,0:05:45.41,0:05:49.58,Default,,0000,0000,0000,,Again, multiply the\Ncoefficients, add the exponents,
Dialogue: 0,0:05:52.66,0:05:55.75,Default,,0000,0000,0000,,and I've got a simplified expression.
Dialogue: 0,0:05:56.66,0:05:59.23,Default,,0000,0000,0000,,Let's get really crazy here,\Nlet's have a little fun.
Dialogue: 0,0:05:59.23,0:06:01.30,Default,,0000,0000,0000,,So we've noticed the pattern,\Nlet's have a little fun.
Dialogue: 0,0:06:01.30,0:06:04.13,Default,,0000,0000,0000,,Just saying, I can, I can do more.
Dialogue: 0,0:06:04.13,0:06:07.13,Default,,0000,0000,0000,,Negative 9x to the fifth power times
Dialogue: 0,0:06:13.37,0:06:16.54,Default,,0000,0000,0000,,negative three, use parentheses there,
Dialogue: 0,0:06:17.66,0:06:19.15,Default,,0000,0000,0000,,when you have a negative in front,
Dialogue: 0,0:06:19.15,0:06:20.42,Default,,0000,0000,0000,,you always wanna use parentheses.
Dialogue: 0,0:06:20.42,0:06:23.17,Default,,0000,0000,0000,,Let's do x to the 107th power.
Dialogue: 0,0:06:25.18,0:06:27.26,Default,,0000,0000,0000,,If I would have showed you\Nthis before this video,
Dialogue: 0,0:06:27.26,0:06:28.64,Default,,0000,0000,0000,,you would have said oh my goodness,
Dialogue: 0,0:06:28.64,0:06:30.74,Default,,0000,0000,0000,,there's nothing I can do, I'm boxed,
Dialogue: 0,0:06:30.74,0:06:32.47,Default,,0000,0000,0000,,there's no way out.
Dialogue: 0,0:06:32.47,0:06:36.08,Default,,0000,0000,0000,,But now you know that it's as\Nsimple as follow the rules.
Dialogue: 0,0:06:36.08,0:06:38.79,Default,,0000,0000,0000,,We're going to multiply the coefficients,
Dialogue: 0,0:06:38.79,0:06:42.17,Default,,0000,0000,0000,,negative nine times negative three is 27.
Dialogue: 0,0:06:42.17,0:06:45.23,Default,,0000,0000,0000,,Two negatives is a positive\Nand nine times three is 27.
Dialogue: 0,0:06:45.23,0:06:47.77,Default,,0000,0000,0000,,I'm gonna add my powers.
Dialogue: 0,0:06:47.77,0:06:51.19,Default,,0000,0000,0000,,Five plus 107 is a hundred, ooh, not two,
Dialogue: 0,0:06:54.44,0:06:58.11,Default,,0000,0000,0000,,that was almost a mistake I made there.
Dialogue: 0,0:06:58.11,0:07:00.67,Default,,0000,0000,0000,,Let's get rid of that, give\Nme a second chance here.
Dialogue: 0,0:07:00.67,0:07:02.66,Default,,0000,0000,0000,,Life's all about second chances,
Dialogue: 0,0:07:02.66,0:07:04.41,Default,,0000,0000,0000,,five plus 107 is 112.
Dialogue: 0,0:07:06.70,0:07:09.42,Default,,0000,0000,0000,,And so, this crazy expression,
Dialogue: 0,0:07:09.42,0:07:12.65,Default,,0000,0000,0000,,which is two monomials, here's the first,
Dialogue: 0,0:07:12.65,0:07:16.86,Default,,0000,0000,0000,,here's the second, when\Nwe multiply and simplify
Dialogue: 0,0:07:16.86,0:07:20.51,Default,,0000,0000,0000,,we get another monomial,\Nwhich is 27x to the 112th.
Dialogue: 0,0:07:20.51,0:07:24.25,Default,,0000,0000,0000,,I'm gonna leave you on a cliffhanger here.
Dialogue: 0,0:07:24.25,0:07:27.59,Default,,0000,0000,0000,,Which, I'm gonna show you a problem.
Dialogue: 0,0:07:27.59,0:07:30.30,Default,,0000,0000,0000,,What variable should we use?
Dialogue: 0,0:07:30.30,0:07:31.78,Default,,0000,0000,0000,,You notice I've been trying\Nto vary the variables up
Dialogue: 0,0:07:31.78,0:07:34.70,Default,,0000,0000,0000,,to show you that it just doesn't matter.
Dialogue: 0,0:07:34.70,0:07:35.96,Default,,0000,0000,0000,,That's an ugly five,\Nlet's get rid of that.
Dialogue: 0,0:07:35.96,0:07:38.55,Default,,0000,0000,0000,,Give me a second chance with that one too.
Dialogue: 0,0:07:38.55,0:07:41.80,Default,,0000,0000,0000,,So let's look at 5x to the third power,
Dialogue: 0,0:07:45.94,0:07:48.28,Default,,0000,0000,0000,,times 4x to the sixth power.
Dialogue: 0,0:07:51.21,0:07:53.39,Default,,0000,0000,0000,,And I'm gonna show you a wrong answer.
Dialogue: 0,0:07:53.39,0:07:55.74,Default,,0000,0000,0000,,I had a student that asked to do this,
Dialogue: 0,0:07:55.74,0:07:58.45,Default,,0000,0000,0000,,and here's the wrong\Nanswer that they gave me.
Dialogue: 0,0:07:58.45,0:08:01.28,Default,,0000,0000,0000,,They told me 9x to the 18th power.
Dialogue: 0,0:08:03.42,0:08:04.42,Default,,0000,0000,0000,,That's terribly wrong.
Dialogue: 0,0:08:04.42,0:08:05.42,Default,,0000,0000,0000,,What did they do wrong?
Dialogue: 0,0:08:05.42,0:08:07.16,Default,,0000,0000,0000,,What did they do wrong?
Dialogue: 0,0:08:07.16,0:08:08.72,Default,,0000,0000,0000,,I want you to think to yourself,
Dialogue: 0,0:08:08.72,0:08:10.05,Default,,0000,0000,0000,,what have we been talking about?
Dialogue: 0,0:08:10.05,0:08:11.72,Default,,0000,0000,0000,,What did they do with the five\Nand the four to get the nine?
Dialogue: 0,0:08:11.72,0:08:13.34,Default,,0000,0000,0000,,What should they have done?
Dialogue: 0,0:08:13.34,0:08:15.93,Default,,0000,0000,0000,,What did they do with the three\Nand the six to get the 18,
Dialogue: 0,0:08:15.93,0:08:18.24,Default,,0000,0000,0000,,and what should they have done?
Dialogue: 0,0:08:18.24,0:08:21.74,Default,,0000,0000,0000,,That's multiplying monomials by monomials.