To determine which expression is equivalent to [tex]\( 4(n - 3^2) + n \)[/tex], let's follow these steps to simplify it.
1. Simplify inside the parentheses:
[tex]\[ n - 3^2 \][/tex]
Since [tex]\( 3^2 = 9 \)[/tex], we get:
[tex]\[ n - 9 \][/tex]
2. Distribute the 4:
[tex]\[ 4(n - 9) \][/tex]
Apply the distributive property:
[tex]\[ 4n - 4 \cdot 9 \][/tex]
[tex]\[ 4n - 36 \][/tex]
3. Add the [tex]\( n \)[/tex] at the end:
[tex]\[ 4n - 36 + n \][/tex]
Combine like terms:
[tex]\[ 4n + n - 36 \][/tex]
[tex]\[ 5n - 36 \][/tex]
So, the expression simplifies to:
[tex]\[ 5n - 36 \][/tex]
Now we match this with the given choices:
- [tex]\( 3n - 6 \)[/tex]
- [tex]\( 3n - 9 \)[/tex]
- [tex]\( 5n - 36 \)[/tex]
- [tex]\( 5n - 144 \)[/tex]
The best answer that matches the simplified expression [tex]\( 5n - 36 \)[/tex] is:
[tex]\[ \boxed{5n - 36} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{5n - 36} \][/tex]
