Algebraic Expressions (Basics) - Free Educational videos for Students in K-12

Algebraic Expressions (Basics) - By Anywhere Math

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00:0-1	variables , coefficients and constant . Oh my . It's
00:03	time to start talking a little bit about algebra .
00:24	Welcome to anywhere . Math . I'm Jeff Jacobson .
00:26	And today we're gonna talk about algebraic expressions before we
00:31	start going over some examples , let's talk about some
00:34	of our terms here . So , first , what
00:36	is an algebraic expression now ? You should remember what
00:40	a numerical expression is because we've talked about that before
00:43	. Uh an expression that includes numbers and operations .
00:46	That's basically it . There's no equal sign . Remember
00:49	expressions have no equal sign , that's equations . Okay
00:54	, um an algebraic expression is different than a numerical
00:58	because it includes variables . So , uh the definition
01:03	and you should write this down an expression that contains
01:05	numbers operations . So if it just has those ,
01:09	then it's just a numerical expression . But if it
01:12	also has one or more variables than all of a
01:15	sudden we're talking about an algebraic expression . So some
01:19	examples X divided by seven , we've got a variable
01:22	. We've got an operation . We got a number
01:24	. Uh same thing here . Three X plus four
01:28	X . Y . You don't see the operation but
01:31	when they're next to each other , that means multiplication
01:33	. So there is an operation . Um So those
01:36	are all examples of an algebraic expression . Uh Some
01:40	that aren't if you've got something like three plus seven
01:46	, that's not an algebraic expression because there is no
01:48	variable . Right ? That would be just a numerical
01:51	expression . Um Same thing if you got three X
01:56	plus four equals 10 . That also is not even
02:02	though it has variable operations , it's got numbers ,
02:07	it has an equal sign , which means this is
02:10	actually an equation . Not an expression at all .
02:13	Okay , so make sure you understand what an algebraic
02:16	expression is and what it includes . Let's talk about
02:20	some more vocabulary words . Here is an algebraic expression
02:25	. five p plus four . We have operations .
02:28	We've got addition five P . That means five times
02:32	piece . So we have multiplication . Uh we have
02:35	numbers , we have a variable . So it's an
02:37	algebraic expression . Now let's talk about the different parts
02:41	of this uh algebraic expression first are the terms and
02:46	the terms are just the parts of the expression .
02:49	So in this case we have two terms , we
02:53	have five p . And we have four . So
02:57	if you had to write down and list what the
02:59	terms were , you would write well five p is
03:02	a term and four is a term . Basically you
03:06	just take out the operations and you list just the
03:09	part of the expression . Okay , um next the
03:13	coefficient . And you can see that kind of color
03:16	coordinated here . A coefficient is the numerical factor of
03:21	a term , right ? One of the parts that
03:24	contains a variable . Well , the only term here
03:27	that contains a variable is the five p . The
03:31	coefficient is the numerical factors . So it's the part
03:36	of the term . It's the number basically uh part
03:39	of the term . So in this case , in
03:43	this expression , the coefficient here is five . Okay
03:49	, you can think of . Well , it's just
03:50	the number in front of the variable . Okay ,
03:52	Just which it is . Right , uh , next
03:56	variable . Well , what is a variable ? A
03:59	variable is just a symbol . Usually we write it
04:01	as a letter and oftentimes it's either X or Y
04:04	because of the coordinate grid . Right ? You have
04:08	the X axis and the Y axis , which is
04:10	why oftentimes you see equations or expressions with X and
04:14	Y . But it can be any any letter ,
04:16	any letter you want . And it represents one or
04:19	more numbers . It's called the variable because it can
04:23	vary in this expression , I can say , well
04:26	let's make P equal to five . Or let's say
04:30	P is equal to three , or P is equal
04:32	to a million . Right ? I can choose whatever
04:34	I want for that . P That's why it's called
04:37	a variable . It can vary . It can change
04:40	. Uh And so in this case are variable blue
04:43	with the blue are variable is pete okay . And
04:49	last but not least is the constant . Now when
04:51	you think of constant things that are constant , are
04:54	things that don't change ? Okay , that's something that's
04:57	constant . Um gravity is a concept , gravity doesn't
05:01	change unless you get out into space . Right ?
05:04	Um So this constant , it's a term with no
05:07	variable . So here are only term with no variable
05:10	. Was the four . That four , No matter
05:13	what I make P that four will always be four
05:17	. It's not going to change . It is a
05:19	constant . So these are the different terms and things
05:23	you should know about . Uh an algebraic expression ,
05:27	let's do an example Example one identify the terms coefficient
05:32	and constant of this algebraic expression first . Let's start
05:37	with the terms . Remember those are the parts and
05:40	if you want to try this on your own ,
05:41	go for it , go ahead and positive video .
05:43	The terms are the parts of this . So we
05:45	kind of take the operations out and the terms ,
05:49	well , we've got a term here and the term
05:51	here . So the terms You have five x and
05:56	you have 13 next the coefficients well , coefficients were
06:02	only looking at the terms that have a variable .
06:05	So coefficients , I'm not even going to bother with
06:07	that . 13 . I'm just gonna look at the
06:11	five x . And then remember , it's the numerical
06:17	part of the term that has the variable . So
06:21	out of this five X . The coefficient is just
06:24	the five and last but not least the constant .
06:29	Remember that's something that doesn't change no matter what the
06:33	variable is . So in this situation the constant is
06:39	at 13 . Okay it doesn't include anything next to
06:44	a variable . Right ? That's the constant . It
06:47	stays 13 . No matter what . Okay . Here's
06:49	something China your own Example to simplify the expression .
07:01	So I have 1.5 times eight times eight times h
07:06	. So hopefully you notice right off the bat you
07:09	have repeated multiplication eight times eight times age . Well
07:13	we know a shortcut . Something that we can simplify
07:16	that into and that's using exponents . I have a
07:19	choice multiplied by itself three times . So that's the
07:23	same as H cute And 1.5 times all of that
07:30	. Well I can get rid of that this multiplication
07:33	symbol and just put them next to each other .
07:35	Right ? That still means the same thing . So
07:37	if I write 1.5 H cube it's exactly the same
07:43	thing . Just simplified . Right ? So that is
07:46	what it would look like . If you simplify that
07:48	expression 1.5 H cube . And in this case 1.5
07:53	would be your coefficient good . Here's some more to
07:58	try on your own . Here's our last example evaluate
08:12	three X -14 when x equals five . So now
08:16	in this situation there telling us exactly what the variable
08:20	is going to be equal to and that's going to
08:22	be five . So my first step is to substitute
08:28	okay to evaluate I'm trying to find the value and
08:33	in order to do that I need to substitute that
08:36	five in for X . Because it's saying X is
08:39	equal to five . So what I'm gonna do is
08:43	I have three . Now a good habit to get
08:46	into is when you substitute use parentheses . All I'm
08:49	doing is replacing that five for the X . I'm
08:51	substituting it in so three times five . Remember three
08:57	X . That means three times X . So I
09:00	have three times five I saw the -14 and now
09:05	it's just order of operations . I have multiplication and
09:08	subtraction . Multiplication comes first , so three times five
09:13	is 15 minus the 14 is one and that is
09:18	my final answer . Here's some more to try on
09:20	your own . Thank you so much for watching and
09:34	as always if you like this video please subscribe .

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