Let's break down the question step-by-step and evaluate the expression given the number [tex]\( n = 3 \)[/tex].
Step 1: Understand key words and their replacements
- Six becomes [tex]\( 6 \)[/tex]
- Times translates to multiplication, [tex]\( \times \)[/tex]
- The sum of indicates an addition operation, [tex]\( + \)[/tex]
- A number is represented by [tex]\( n \)[/tex]
- Cubed means raising the number to the power of 3, [tex]\( n^3 \)[/tex]
- Two remains as [tex]\( 2 \)[/tex]
Step 2: Form the expression
Using the replacements mentioned above, the expression "six times the sum of a number cubed and two" can be written mathematically.
So, we have:
[tex]\[ 6 \times (n^3 + 2) \][/tex]
Step 3: Simplify the parenthesis
Now let's substitute [tex]\( n = 3 \)[/tex] and simplify.
First, compute the sum inside the parentheses:
[tex]\[ n^3 + 2 \][/tex]
[tex]\[ 3^3 + 2 \][/tex]
[tex]\[ 27 + 2 \][/tex]
[tex]\[ 29 \][/tex]
Step 4: Multiply by 6
Next, multiply the sum by 6:
[tex]\[ 6 \times 29 \][/tex]
[tex]\[ 174 \][/tex]
Step 5: State the value of the expression
The value of the expression when [tex]\( n = 3 \)[/tex] is:
[tex]\[ \boxed{174} \][/tex]
This verifies that the statement "The value of the expression is 174" is correct. Therefore, the correct value of the expression is [tex]\( \boxed{174} \)[/tex].
