To find which expression is equivalent to [tex]\(4(n - 3^2) + n\)[/tex], we can simplify the given expression step-by-step. Here's how to do it:
1. Expand the Expression:
Start by evaluating the term inside the parentheses:
[tex]\[
3^2 = 9
\][/tex]
So,
[tex]\[
n - 3^2 = n - 9
\][/tex]
Now multiply by 4:
[tex]\[
4(n - 9) = 4n - 36
\][/tex]
2. Combine Like Terms:
Next, we add [tex]\(n\)[/tex] to the result:
[tex]\[
4n - 36 + n
\][/tex]
Combine the [tex]\(n\)[/tex] terms:
[tex]\[
4n + n - 36 = 5n - 36
\][/tex]
Therefore, the simplified expression is [tex]\(5n - 36\)[/tex].
3. Compare to the Given Choices:
Let's compare this simplified form to the provided options:
[tex]\[
\begin{array}{ll}
1) & 3n - 6 \\
2) & 3n - 9 \\
3) & 5n - 36 \\
4) & 5n - 144 \\
\end{array}
\][/tex]
Clearly, [tex]\(5n - 36\)[/tex] matches one of the given choices exactly.
So, the expression equivalent to [tex]\(4(n - 3^2) + n\)[/tex] is:
[tex]\[
\boxed{3}
\][/tex]
