Terms in a linear expression are called like terms if their variable part is the same. For example, in the linear expression
the terms and are like terms because both terms contain the same variable
A linear expression may also contain multiple groups of like terms. For example, in the expression
we have two groups of like terms:
- and are like terms because they all contain the variable
- and are like terms because they both contain the variable
Remember: When a term has a subtraction symbol in front of it, the term is treated as a negative.
List the like terms for the expression
We write the terms of the expression as follows:
We see two pairs of like terms:
- The terms and are like terms since they both contain the variable
- The terms and are like terms since they both contain the variable
What are the like terms in the expression $5a - 9b - 7a + 2c?$
|
a
|
No like terms |
|
b
|
$5a$ and $-7a$ |
|
c
|
$5a$ and $7a$ |
|
d
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$5$, $-9$, $-7$, and $2$ |
|
e
|
$5a$, $-9b$, $-7a$, and $2c$ |
What are the like terms in the expression $3x + 2y + z - y?$
|
a
|
No like terms |
|
b
|
$2y$ and $-y$ |
|
c
|
$3,$ $2,$ $1,$ and $-1$ |
|
d
|
$2y$ and $y$ |
|
e
|
$3x,$ $2y,$ $z,$ and $-y$ |
In some expressions, there are no like terms. For example, in the expression there are two terms, and . These two terms do not have the same variable part, so they are not like terms.
List the like terms for the expression
We write the terms of the expression as follows:
None of these terms have the same variable part. Consequently, there are no like terms in this expression.
What are the like terms in the expression $4 - 13x - 2y - 5z?$
|
a
|
$-13x$ and $-5z$ |
|
b
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$-13x$ and $-2y$ |
|
c
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$4$ and $-5z$ |
|
d
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$4$ and $-13x$, $-2y$ and $-5z$ |
|
e
|
No like terms |
What are the like terms in the expression $3a + 4b - 5 + 8c?$
|
a
|
$3a$ and $4b$ |
|
b
|
$4b$ and $8c$ |
|
c
|
$-5$ |
|
d
|
No like terms |
|
e
|
$3a,$ $4b,$ and $8c$ |
Constants are like terms, even though they do not contain variables.
To understand why this is, remember that two terms are called like terms if they share the same variable part.
All constants have no variables, so technically they do share the same variable part. Their variable part consists of no variables at all!
What are the like terms of the expression
We write the terms of the expression as follows:
There are two groups of like terms:
and are like terms because they all contain the variable
and are like terms because they both contain no variable.
How many pairs of like terms are in the expression $1 + 2a - 3 + 4a - 5b?$
|
a
|
$1$ |
|
b
|
$2$ |
|
c
|
$4$ |
|
d
|
$3$ |
|
e
|
$0$ |
How many pairs of like terms are in the expression $a + 2b + 3 - 10b - 9 - 8a?$
|
a
|
$4$ |
|
b
|
$0$ |
|
c
|
$1$ |
|
d
|
$2$ |
|
e
|
$3$ |