Sure, let's break this problem down step by step.
### Step 1: Write the Algebraic Expression
The problem states:
"Three less than the sum of nine and a number cubed."
Let's denote the unknown number as [tex]\( n \)[/tex].
1. First, calculate the number cubed: [tex]\( n^3 \)[/tex].
2. Next, find the sum of nine and this cubed value: [tex]\( 9 + n^3 \)[/tex].
3. Finally, subtract three from this sum: [tex]\( (9 + n^3) - 3 \)[/tex].
So, the algebraic expression is:
[tex]\[ (9 + n^3) - 3 \][/tex]
Let's simplify this expression. The simplified version is:
[tex]\[ n^3 + 6 \][/tex]
### Expression
[tex]\[ n^3 + 6 \][/tex]
### Step 2: Determine the Value When [tex]\( n = 2 \)[/tex]
Now, we substitute [tex]\( n = 2 \)[/tex] into the expression [tex]\( n^3 + 6 \)[/tex].
1. Calculate [tex]\( 2^3 \)[/tex]:
[tex]\[ 2^3 = 8 \][/tex]
2. Plug [tex]\( 2^3 \)[/tex] into the simplified expression:
[tex]\[ 8 + 6 \][/tex]
3. Perform the addition:
[tex]\[ 8 + 6 = 14 \][/tex]
### Value
[tex]\[ 14 \][/tex]
So, the algebraic expression representing "three less than the sum of nine and a number cubed" is [tex]\( n^3 + 6 \)[/tex]. When [tex]\( n = 2 \)[/tex], the value of this expression is 14.
