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How To Simplify Algebraic Expressions: Terms, Like Terms, Constants, Coefficients
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Feb 19, 2025
In section 4.1, we learned how to use the distributive property, and that lesson is foundational to our current lesson. In this lesson, we'll learn how to simplify algebraic expressions, but in order to do that, we must first learn how to understand parts of an algebraic expression i.e. terms, like terms, constants and coefficient. and learn how they combine together to facilitate simplifying complex algebraic expressions. Chapters: 00:00 Introduction 01:18 What are the parts of an algebraic expression 09:10 How to identify like terms 11:27 Example: Finding parts of an expression 17:24 How to simplify an expression
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0:00
all right so good morning and then today
0:03
we're going to talk about simplifying
0:05
algebraic expressions like I said I want
0:08
everybody to take notes because this is
0:10
important right so remember everything
0:12
that we've been talking about since the
0:14
beginning is coming down to this here
0:17
next chapter is going to be how to solve
0:22
equations you know that we getting there
0:24
we getting Clos right we getting close
0:26
to equations so
0:28
um um Monday we talked about how do you
0:32
uh Use
0:34
the distributive law a property and you
0:37
can go back to that now this is also
0:39
going to add on to what we've learned
0:41
already because we're going to have some
0:42
distributive property going on here
0:44
right so now what is an expression we've
0:47
already talked about an expression we
0:49
we've already talked about algebraic
0:50
expressions we mentioned all of that so
0:52
today we're going to talk about how to
0:54
simplify them I've mentioned like terms
0:57
remember the other day when we were
0:58
talking about when you have something
1:00
like 3 * x + 5 and we get 3x + 15 how
1:04
you can't add those two because you have
1:07
three x's and you have 15 those are not
1:10
like terms so this is what we're going
1:11
to discuss today okay so the first thing
1:14
that we need to know is this we need to
1:15
know the part of an algebraic expression
1:20
right so this is called an algebraic
1:22
expression you have in the X's you have
1:26
numbers okay this is an algebraic
1:28
expression and the term terms the first
1:31
ter the first thing that we're going to
1:32
learn is the new vocabulary is the word
1:35
the word term so what is the term a term
1:39
is if you look at the expression here
1:41
right each time there is uh a variable
1:46
and a number or just a number that's
1:47
separated by uh an addition sign or a
1:51
negative sign or subtraction sign what
1:53
you have is called the terms so these
1:55
are the terms so
1:57
explaining these here are terms okay
2:01
they are separated by the
2:04
signs okay these are terms so how many
2:07
terms do I have here let's count four
2:10
right 1 2 three and four we have four
2:12
terms yes why the X's terms why the X's
2:15
are terms oh wait anything that is
2:17
separated by a sign is a term I thought
2:19
that was multiplication does that make
2:21
sense no that's not a multiplication
2:23
that's a x right so I have one two three
2:26
and and four so the terms are always
2:30
separated by what the signs right so
2:34
these are the terms so we've checked
2:35
that off our list we know what the term
2:37
is okay now the next thing we're going
2:39
to learn is a new vocabulary is a
2:42
constant does anybody know what a
2:44
constant is no no all right a constant
2:48
is a number that does not have a
2:51
variable a number that does not have an
2:53
X or Y so how many constant do we have
2:55
here two two what are they x x
3:00
they don't have constant don't have x
3:03
two and seven right so we have two
3:05
constants we have two and seven right
3:08
constant again are numbers that do not
3:11
have variables attached to them they
3:14
don't have any variables attached to
3:16
them so we have two and seven two and
3:18
seven are your only constants okay now
3:21
the next term we going to learn is the
3:25
coefficient coefficient all right
3:28
coefficient someone called constant
3:31
constant yeah constant the constant is
3:34
the numbers that do not have attached to
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them any numbers that are not attached
3:39
to any number no numbers that are not
3:41
attached to variables right so two is by
3:44
itself right just think of it think of
3:47
it as a single man or a single woman
3:50
right two is just two seven is just
3:52
seven now 3x is attached three is
3:54
attached to
3:55
what x right and then X is attached to
4:00
nothing one right remember when we don't
4:03
have anything it's always a one right so
4:06
you could read this as 1 x is that make
4:08
sense right so 2 and seven are the only
4:11
constant because they have nothing that
4:13
is attached to them does that make sense
4:16
you everybody to get that yes every you
4:20
got it how many constants do I have in
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here two what are they 2 2 and7 good all
4:26
right now the coefficient the
4:28
coefficient is the
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number right that is tied to the
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variable does that make sense
4:36
that constant c o n s t a n t the
4:40
constant right the coefficient is the
4:43
number that is followed by a variable
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does that make sense right the
4:50
coefficient is a number that is followed
4:53
by the variables so how many coefficient
4:55
do I have here what's that word comp
4:57
coefficient c o e f f i c i e a e n t
5:02
coefficient right coefficient is the
5:05
number that is followed by a variable so
5:08
how many do I have here um alen two what
5:12
are they three three
5:14
and you got it but you almost got is
5:17
when there's no what's the number one
5:19
right one No One X just one right so we
5:21
have two coefficients is three and what
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and one because this is a coefficient
5:27
and also a coefficient here this is
5:29
called imaginary one yes um do we write
5:33
like 3x or just one yes just you can
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write the number the number you write
5:38
one right coefficients are one and three
5:41
coefficient always are followed by a
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variables coefficient are followed by a
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variable yeah right a coefficient is
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followed for example 5 y what's the
5:51
coefficient here five five right what
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about uh y what's the coefficient one
5:57
one right so the coefficient is always
6:00
followed by a variable a Conant is not
6:04
followed by any number it's just
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Standalone does that make sense you see
6:07
the distinction with the coefficient and
6:09
the variable right the coefficient is
6:12
followed by an X or Y or Z or whatever
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the the the letter is but the constant
6:18
has nothing it's just a number that make
6:20
sense all right now the next thing we're
6:23
going to learn is like terms right like
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terms new vocabulary like terms are not
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uh the the terms that look alike right
6:33
like terms so let's say we going to do a
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life term in this classroom so the like
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terms are going to be what we going to
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have boys and girls girls girls so like
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terms here is going to be me
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ebener Gabe and Dexter we are only the
6:50
like terms we are we are all boys right
6:52
we all boys right and then the like
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terms the other like terms are going to
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be with all the girls Laura Lena Emily
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Liz Abigail
7:04
Danielle Vicki Kinsley and Kenzie those
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are going to be the other like terms
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okay so you guys are also together and
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we have to get it we are not the same we
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are not so you can add boys and girls so
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to speak because we are not technically
7:19
like terms you see what I'm saying right
7:21
so like terms are terms that look alike
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so how many lik terms do I have here
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that's totally obvious two seven like
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terms right 2 and seven are together and
7:31
who else is
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together 3x and 1 x how are those like
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terms they have an
7:39
x two and seven are also like terms
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because can you add two and seven can
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you add two plus seven what do you
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get that's right you have two and seven
7:52
are called like terms because you can
7:54
put those two together right they look
7:56
the same they are constant
8:00
does that make sense they are constant
8:01
so you can add the constant together now
8:05
3x and 1X are also like terms because
8:08
can you do 3x + 1 x can we do that yes
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or no
8:13
Vicki are you with me uh what's 3x + 1
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x 4x what that's right 4X what's three
8:22
oranges plus 1 orange you have three
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orang four oranges four oranges right
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foures very simple yeah four
8:30
that's all you're doing the life terms
8:31
are the terms that look the same right
8:34
they look alike so let's do some
8:36
examples here so you guys can understand
8:38
all right now we're going to go up here
8:41
and then we're going to learn how to
8:42
identify like terms we're going to learn
8:45
how to identify them right so if you
8:47
look here first of all before we even
8:50
solve it how many terms do I
8:53
have Kinsley how many terms do I have in
8:56
here just terms not like terms how many
8:59
terms terms I
9:01
have three three right because the terms
9:04
are separated
9:05
by the signs right so we have one two
9:08
and three terms now how many like terms
9:12
do I
9:14
have two two what are they 3x 4X we have
9:18
not just 3x what negative righta - 3x
9:23
and 4x those are like terms like terms
9:28
right
9:30
anybody doesn't understand like terms
9:32
all right like terms think of it this
9:34
way right if I have let me reite this
9:38
as3 oranges right o r is oranges plus
9:42
four apples a right plus four oranges
9:47
right so can you mix apples and
9:52
oranges no can you mix oranges and
9:54
oranges yeah yes so those are like terms
9:58
does that make sense now
10:00
so because they have the same variable
10:02
they have the same variable that's they
10:05
have the same variable same variable
10:07
like terms I like terms when they have
10:09
the same variable yeah I like the way
10:11
you define it for yourself ready ma no
10:13
you don't you not right that unless you
10:14
want
10:15
to section yeah you writing everything
10:18
that's here like terms are 3x and 4x
10:22
numbers that have the same variables or
10:24
numbers that look the same right I like
10:25
the way you defin it you even did better
10:27
a better job than I did good
10:30
now here gab how many terms do I have in
10:34
this
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expression four four right I have 1 2
10:41
three and four how many like terms do I
10:44
have
10:45
here identify them for
10:52
me - 5 is 10 and then
11:00
I already have this so what else do I
11:02
have
11:03
left three and four right because I can
11:05
combine them they are the same they are
11:07
numbers right they are constant does
11:09
that make sense are we on the same
11:12
picture guys all right those are
11:14
constant and these are like terms okay
11:16
they all like terms now now in this uh
11:20
second example we're going to learn how
11:21
to identify parts of an expression right
11:25
so what I want you all to do is this
11:27
identify what the terms the terms the
11:30
coefficient and the constant yes um in
11:35
in the first equation we only we only
11:38
have 3x and 4x listed we not list 4 y
11:42
because it's just one yeah it's just one
11:44
okay so 4 y by itself so there's no
11:46
other term that's like that has a y next
11:48
to it right so yes yeah that's a good
11:50
good good observation now here how many
11:53
terms I have so let's let's put it
11:55
together here terms how many terms we
11:57
have
11:58
Danielle um
12:00
and this one
12:01
here one two three four four terms does
12:06
everybody age that we have four terms
12:08
right because we have 1 2 three and four
12:11
four terms here correct all right four
12:15
terms now the next question is how many
12:18
like terms do I
12:22
have Dan you still huh two two what are
12:27
they they are 6 6x X 6x and X thank you
12:33
now how many coefficients do I have
12:37
one are you sure we have only one
12:39
coefficient what is the definition of a
12:40
coefficient who knows numbers that that
12:43
are not sorry number that are always
12:46
followed by a variable okay so how many
12:48
numbers are followed by a variable here
12:50
one two three so what are they um 6X you
12:54
don't say 6X just six right six two not
12:58
not two what is it
13:02
oh2 right it's not two is negative
13:04
because you have to take into
13:05
consideration the sign that's next to it
13:07
right -2 and then what else and then X
13:11
what's next to the X a negative no
13:14
what's next to POS one positive what one
13:18
one right so is one one that make sense
13:22
all right and now how many
13:24
constants do I have here constant what's
13:28
the definition of a Conant
13:32
that are always attached to a variable
13:34
huh numbers that are always attached to
13:35
aable that's not the
13:38
constant numbers that is by itself with
13:41
nothing else to it so what is it
13:44
here what is it five is it five or neg
13:47
five you got to be careful here you have
13:50
to see the sign that's next to it it's
13:51
NE five all right we have to also take
13:54
into consideration the number the sign
13:56
that's next to yes
13:59
so it looks like x - 5 yeah it's it's
14:02
like + 1 x +5 okay pretty pretty much
14:06
right X is just yeah X is 1 X +5 so the
14:12
constant is5 so you always have to take
14:15
into consideration the sign that's next
14:17
to it yes
14:19
mhm uh okay so like when we're listening
14:22
to Y is ne2 yeah -2 yeah -2 y yeah so
14:26
let me give you another example we're
14:28
going to identify this here so I have
14:31
say I have
14:33
um -10 X -
14:38
2 + 6 y - 5
14:45
y
14:47
- 6 x - x all right I know I made
14:53
complicated but that's okay
14:56
minus yeah cuz the minus is what nobody
14:59
x minus is right how many terms do I
15:00
have
15:02
here Kenzie how many terms do I have
15:06
let's count them what are we looking
15:08
at I'm I'm looking at the terms the
15:11
terms are how many terms any anything
15:13
that's separate by a sign so how many do
15:15
I have here let's count
15:16
it x 6 5 y 6 y
15:22
-2- so how many is
15:24
that
15:27
1 4 five six right so Ken is still how
15:31
many now I want to know how many like
15:33
terms do I have L them one one at a
15:38
time x and 6X so you don't just say x
15:42
and 6X you have to look at the sign next
15:44
to it right so what is
15:47
it
15:50
negative and then negative and
15:55
then 10 x - 10 x there you go and then
15:59
what else do we have any other like
16:00
terms 6 y yeah 6 Y
16:03
and Y 5 y thank you very much right
16:07
anything else that's like
16:09
terms no no right that's it now how many
16:12
coefficients do I have
16:15
Coe coefficients are numbers that are
16:18
followed by variables okay so how many
16:21
do I have
16:23
here y so - 10 right 10 mhm no you don't
16:29
you don't pronounce the X just A1 right
16:32
what
16:33
else
16:36
MH
16:38
56 mhm and then onega 1 right was
16:43
negative 1 all right yeah um wouldn't 6
16:46
y
16:47
and5 y also be like ter yeah we did
16:51
mention it 6 y
16:54
y they like terms we mentioned them yeah
16:56
we did Y and now how many constants do I
16:59
have here have how many constants do I
17:02
have constant is just a standard RO
17:05
number one what is it or -2 thank you -2
17:11
now we more clear on this now does that
17:13
make more sense or still
17:15
confusing all right right so we just
17:18
have to figure out the way that works
17:20
for you now the next thing we're going
17:21
to learn how to do is this we know we
17:23
going to learn how to simplify an
17:25
expression right simplify an expression
17:27
so to simplify an expression we need to
17:29
use some things here that we're going to
17:30
learn some techniques right so I have 4x
17:33
+ 6 +
17:35
2x how can I make this simple I mean I
17:38
cannot boil you down to a simpler term
17:39
yes um start with putting the like terms
17:43
together that's right x + 2x that's
17:46
right I know how to make this simple
17:48
right so what do you get oh you don't do
17:51
it um nothing this
17:53
last yes all right so here did you hear
17:57
what she say to com to simplify this we
18:00
have to find first the like terms why do
18:03
we have to find the like terms because
18:04
we can put those two two together does
18:07
that make sense so what are the like
18:08
terms here
18:10
Alena 4X and 2x so we're going to go 4X
18:14
right + 2x + 6 so do you see what I did
18:18
I rearranged it so I can put these two
18:20
together does that make sense are we
18:23
good on that is everybody good on that
18:25
yes or no yeah all right so now what's
18:29
4x +
18:31
2x 6 x right four four oranges plus two
18:35
oranges are six oranges right so I got
18:37
6X + 6 am I
18:39
done no yes yes or no yes cuz can I
18:43
combine these into two I they like terms
18:46
no they not like terms so I cannot put
18:47
these two together because they are not
18:50
like terms right these two cannot be put
18:53
together because they are not like terms
18:55
so now how many terms do I have in this
18:57
expression
18:59
next how many
19:01
terms do I have this expression here I'm
19:03
just asking simple question how many
19:05
terms do I have two two right two two
19:08
terms how many like terms do I have in
19:11
this
19:12
expression you have any like terms none
19:15
how many constants do I have here one
19:19
what is it six and how many coefficients
19:22
do I
19:23
have six not 6X six right is you don't
19:27
pronounce the X just uh now that's next
19:29
to all right good now Lina you're next
19:31
you help me with this one so now again
19:35
I'm trying to put these two together
19:36
right so can I rearrange it so I can put
19:39
a life term together what do I do
19:42
here so how do I rewrite this so I can
19:45
simplify
19:47
it 5 y
19:52
uhhuh minus y do you see what we did
19:55
here these are the like terms right so
19:58
we 5
19:59
Yus y because I always consider the sign
20:03
that's next to it behind it right 5 y -
20:08
Y and then now what plus what 2 and then
20:13
- 6 we see how we rearrange it right
20:16
we're going to put the like St together
20:18
and the way you do it is you always have
20:20
to pay attention to the sign that is
20:23
next to it yes so um in equation is
20:27
written like that Can You Solve It by
20:29
switching it around so yeah okay you
20:31
switch it around so that way you can put
20:33
the like together right it goes five Y
20:35
is here by seven on the ey negative y
20:38
yeah I want to put these two together
20:39
but to put them together I have to make
20:41
sure I'm respecting what the sign that
20:43
is next to them
20:46
yes when I
20:51
it that's also fine you can do that too
20:55
I actually recommend it 5 y + y right
20:58
yeah yeah you can do that too so if that
21:00
makes sense you can go if you want to
21:01
just go step by step and put 5 y + y
21:04
That's fine right but if you want to
21:07
just burn those steps you can go 5 y - Y
21:10
and then 2 - 6 right the reason why is
21:14
because a lot of time people get hung up
21:16
they forget that they don't know how to
21:18
like combine the like terms you always
21:20
have to look at the the number that's
21:22
next to it right 5 y - y because I have
21:25
5 y andus y so I put those two together
21:28
and I have 2 - 6 yes when I use this in
21:31
my yes you find out soon when you find
21:35
out soon what's 5 y
21:38
[Music]
21:43
y y I have five oranges I take away one
21:47
orange how many oranges I four so 5 y -
21:52
Y is 4 y right 4 Y and what's 2 - 6 four
21:59
what
22:01
what4 - four
22:04
right smart see everything is coming
22:07
together everything that we've been
22:08
doing since the beginning of this is
22:10
coming together yeah um the way I did it
22:13
I got for y
22:15
plus4 should I simplify that to 4 Yus 4
22:19
yeah okay cuz you have a positive and a
22:21
negative it gives you a negative right
22:22
all right now I know you're not going to
22:25
like this one I can tell I know it's not
22:27
going to be something
22:29
CRA right now guess how we going to do
22:33
this watch how we're going to do this
22:35
right do not hate on me please just be
22:39
patient all right so I have 6 y here
22:42
right and I have minus three right now
22:46
look pay attention you remember what we
22:48
worked on the distributive property
22:51
distributive property we're going to
22:53
apply it here right so if I'm here
22:56
watch I'm going to do what
22:59
-3 *
23:02
what all right are you all seeing
23:05
this -3 * X
23:09
first so -3 * X and then -3 *
23:16
what
23:17
2 -2 y
23:21
right or there's two ways we did this
23:24
some people just go3 and2 and they get
23:26
plus which is fine I've seen some of
23:29
y'all do that you can do that or if you
23:31
want to
23:32
be on the S side of things you can just
23:36
go - 3 right time -2 y like this
23:45
okay so that gives you 6 y - 3x and I
23:50
have -3 * -2 Y what what does that give
23:54
me yeah is it a negative and a negative
23:58
are positive so I get what 5 y you're
24:02
multiplying oh uh 6 y 6 y all right now
24:08
how many lik terms do I have in
24:12
here two what are they 6 Y and 6 y so
24:17
I'm going to put those two together so
24:18
I'm going to rewrite this as 6 y + 6 y -
24:22
what
24:24
3x okay and I what 6 y + 6 y
24:33
Laura y right minus what 3x and and I
24:39
can stop here so we're going to spend H
24:42
I know it's a little bit confusing but
24:44
that's
24:45
fine we're going to sit on this for a
24:47
little bit we're going to sit on for
24:48
maybe like three more days to make sure
24:50
everybody gets it and then we going to
24:51
move on to the next no all right so
24:54
we're going to sit on this for a little
24:55
bit I like your area
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