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 6 to the terms inside the parentheses.
Since 6n and 24 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+24?
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+24?
A
3(2n+6)
3(2n)+3(6)
6n+18
No
C
3(2n+8)
3(2n)+3(8)
6n+24
Yes
We found that the expression from option C is equivalent to the given expression!
