We are asked to match the given expression with an equivalent expression. First, we will simplify it. To do it, we will use the Distributive Property. We will distribute 2 to the terms inside the parentheses.
Since $6n$ and $18$ are not like terms, the expression cannot be simplified further. Now let's take a look at the possible equivalent expressions.
Option
Expression
Is It Equivalent to $6n+18?$
A
$3(2n+6)$
?
B
$6n+9$
No
C
$3(2n+8)$
?
D
$6n+12$
No
We can already tell that the expressions B and D are not equivalent to our expression. It is because they are all in simplest forms and they are not the same as our expression! The expressions A and C can be simplified further.
Option
Expression
Use the Distributive Property
Multiply
Is It Equivalent to $6n+18?$
A
$3(2n+6)$
$3(2n)+3(6)$
$6n+18$
Yes
C
$3(2n+8)$
$3(2n)+3(8)$
$6n+24$
No
We found that the expression from option A is equivalent to the given expression!
