Question

Which expression is equivalent to [tex][tex]$4(n-3^2)+n$[/tex][/tex]?

A. [tex]3n-6[/tex]
B. [tex]3n-9[/tex]
C. [tex]5n-36[/tex]
D. [tex]5n-144[/tex]



Answer :

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]