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Algebraic Expressions (Advanced) - By Anywhere Math

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00:0-1	Welcome to anywhere , Math . I'm Jeff , Jacobson
00:01	and today we're learning all about algebraic expressions . Let's
00:06	get started . Alright before we get to our first
00:26	example , let's talk a little bit about the vocabulary
00:29	involved with algebraic expressions . The algebraic part means that
00:33	we're gonna have variables in the expressions and then because
00:36	their expressions means there's gonna be no equal sign right
00:39	. If it had an equal sign then we'd be
00:41	talking about equations . But for today just algebraic expressions
00:45	. Now , the first word we're going to talk
00:48	about our terms in terms are the parts of an
00:52	expression and algebraic expression . Not the operations . Next
00:56	life terms are terms that have the same variables but
01:00	also raise the same exponents . If you have an
01:03	X and A Y . Those are not like terms
01:06	because there not the same variables . If you had
01:10	an X squared and X cubed . Well those are
01:14	the same variables but they're not raised the same exponents
01:17	. So they also would not be like terms ,
01:20	Okay , last word is constant terms . Or just
01:24	constants . And constants are also like terms but they
01:27	have no variables . They're called constants because no matter
01:30	what the value of the variables are , they stay
01:33	constant , they stay the same . Now let's get
01:36	into our first example example one identify the terms and
01:39	the like terms in each expression . So for a
01:42	we've got nine x minus two plus seven minus x
01:47	. So again , this is an algebraic expression because
01:50	we have variables . Uh And then first thing I'm
01:54	gonna do is I'm going to identify the terms well
01:57	to do that . What I want to do first
01:59	is change this into strictly an addition expression . So
02:04	whenever I have subtraction , I'm going to change that
02:07	to addition , adding the opposite . I'm gonna rewrite
02:10	this as nine X . Instead of minus two ,
02:14	I'm gonna say plus a negative to . Uh and
02:17	then plus seven . That's ok . And then instead
02:19	of minus X , you probably could guess it plus
02:23	negative eggs . So my first step is just to
02:27	rewrite uh the expression as an addition expression . Now
02:32	I'm ready to identify the terms . And again the
02:34	terms are the parts of the expression without the operations
02:40	. So the terms then are nine X . Negative
02:43	27 and negative X . Those are my terms .
02:48	My life terms are where I have the same variables
02:53	raised to the same exponents or constants . I have
02:57	a nine X . And a negative X . They're
02:59	both X . It doesn't matter that this is negative
03:02	. That's okay . The fact is that both of
03:04	these are raised to the first power . Even though
03:07	we don't write it , there's just one X .
03:09	Okay so those are like terms nine X . And
03:13	negative X . I'll put a comma my other group
03:17	of like terms are my constant negative two and 78
03:21	of two and seven . Ok . Part B .
03:25	I'm gonna do slightly different . Um I could do
03:28	the same thing and just change it first to an
03:30	addition expression again . But I'm gonna circle . And
03:35	this is another strategy that a lot of students like
03:38	to use . You just circle the parts of the
03:41	expression . And if you see a negative or a
03:44	subtraction in this case right now you include that with
03:48	whatever is after it . So I'm gonna use that
03:50	strategy here . So I have W squared . Whenever
03:53	I see A plus , I'm not going to circle
03:55	that I have a five W . I have minus
03:59	three W squared . So I'm gonna circle . When
04:02	I see that subtraction , I'm going to include that
04:04	with what comes after it . And then I'm going
04:07	to have that w Now I want you to see
04:10	how it's similar to what we did here . If
04:11	I changed this expression too . Uh In addition expression
04:15	, this is what I would get , I would
04:17	get W squared plus five W . And then remember
04:21	subtraction , we would change that to plus a negative
04:25	three W squared . And then plus W . Again
04:28	notice my terms , W Square W squared . Five
04:32	W . Five W . Negative three W squared ,
04:35	negative three W squared W . And W . So
04:39	a lot of students like to use this and if
04:42	that works for you , then great . So let's
04:44	list our terms . We have W squared five W
04:49	. Uh negative three W squared . And w now
04:55	let's do our like terms . So again , we're
04:57	looking if you notice they're all w . But then
05:00	we also have to check to make sure they have
05:02	the same exponents . So I've got W squared here
05:05	and a negative three W squared here . It doesn't
05:08	matter with this coefficient . That's okay . These are
05:11	still like terms because there w squares . Uh So
05:16	that's my first W square it and native three W
05:21	squared . And then we've got five W and W
05:23	. Again the coefficient is okay , We're just looking
05:27	at the same variable in this case , the race
05:30	to the first power . So 5W&W . Those are
05:34	my other like terms . Let's look at another example
05:39	. Alright example , to simplify 3/4 Y plus 12
05:43	minus one half Y minus six . Okay , well
05:47	first I know how to simplify fractions , right to
05:50	six would become one third . But what about simplifying
05:54	algebraic expressions ? How do I know when it's in
05:58	simplest form ? When there are no like terms and
06:02	no parenthesis ? When you get to that point ,
06:06	then you've simplified it far enough . It's in simplest
06:09	form . And to get there we call it combining
06:12	like terms . So what we just identified when you
06:15	see like terms , we can combine them . Um
06:18	and use the distributive property when you need to .
06:20	That's gonna help you get rid of the parentheses .
06:22	So let's try example to I'm going to change it
06:25	to an addition expression . So this is gonna become
06:29	3/4 . Why ? Plus 12 ? That's already addition
06:33	. This minus is gonna be plus a negative one
06:37	half Why ? And then that minus six becomes plus
06:41	negative six . And the reason we do that is
06:43	because now I can change the order . The community
06:46	of property of addition means I can change the order
06:48	around because I have all addition . So I'm gonna
06:51	rewrite it 3/4 . Why switch this around ? Plus
06:56	negative one half , y plus 12 . And then
07:00	plus by negative six . Now we're ready to combine
07:06	like terms . This would become negative to uh force
07:10	why ? That's the same thing . So when I
07:13	add that with 3/4 wide , that would give me
07:15	1/4 Y plus 12 and negative six . We become
07:21	six at this point . Are there any like terms
07:26	? No , that's a constant and that has a
07:28	variable of why they're not like terms . Are there
07:31	any parentheses , nope . Which means this expression here
07:37	is now in simplest form . Here's some to try
07:41	on your own . All right , for the last
07:48	example simplify this expression Now again to get it in
07:53	simplest form we're looking for No like terms and no
07:56	parentheses . And to get there we combine like terms
07:59	and use the distributive property when necessary . Whenever you
08:02	have parentheses . First thing to always look for and
08:06	if you want to put a big star next to
08:07	this , see if you can simplify in the parentheses
08:10	first 16 plus four I can't they're not like terms
08:14	. So that's okay . So now here hopefully you
08:17	recognize you're gonna use that distributive property and if you
08:21	don't remember how to do that , check out this
08:23	video but we're going to distribute this negative one half
08:26	to everything inside the parentheses first . So negative one
08:29	half times six N . Negative one half times four
08:33	negative one half times six . N plus negative one
08:37	half times four . And then we still have that
08:41	plus to end . Make sure you always show your
08:44	work going down nice and organized . Now we just
08:47	start to simplify negative one half times six . N
08:50	. That's gonna be negative three N . Plus negative
08:53	one half times four is gonna be negative too .
08:57	And then I still have that too in now here
09:00	let's combine like terms . Well negative two is the
09:03	only constant . So that's going to be off by
09:05	itself negative three in And to end our like terms
09:10	, they're both just end and they're both just to
09:12	the first power negative three . End plus to end
09:15	would be negative one end which I'll just write it
09:19	just negative end plus negative two . Lastly remember we
09:24	can't have parentheses . So at this situation I know
09:28	it's kind of weird because we we typically like to
09:31	have addition . I'm going to change it back to
09:34	a subtraction problem . So this becomes negative end -2
09:40	. There are no like terms and there's no parenthesis
09:43	anymore . So this is in simplest form here's some
09:46	more to try on your own as always . Thank
09:54	you so much for watching and if you like this
09:56	video please subscribe . Yeah .

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