To find the product [tex]\((n - 6)(3n - 6)\)[/tex], we can use the distributive property of multiplication over addition, also known as the FOIL method (First, Outside, Inside, Last). Let's break this down step by step:
First, let's write down the expression:
[tex]\[
(n - 6)(3n - 6)
\][/tex]
1. First: Multiply the first terms in each binomial:
[tex]\[
n \cdot 3n = 3n^2
\][/tex]
2. Outside: Multiply the outside terms:
[tex]\[
n \cdot (-6) = -6n
\][/tex]
3. Inside: Multiply the inside terms:
[tex]\[
-6 \cdot 3n = -18n
\][/tex]
4. Last: Multiply the last terms in each binomial:
[tex]\[
-6 \cdot (-6) = 36
\][/tex]
Next, we add all these results together:
[tex]\[
3n^2 - 6n - 18n + 36
\][/tex]
Combine like terms (the terms with [tex]\(n\)[/tex]):
[tex]\[
3n^2 - 24n + 36
\][/tex]
Therefore, the product of [tex]\((n - 6)(3n - 6)\)[/tex] is:
[tex]\[
3n^2 - 24n + 36
\][/tex]
So, the correct answer is:
[tex]\[
3n^2 - 24n + 36
\][/tex]
This matches option 2. Thus, the correct choice is:
[tex]\[
\boxed{3n^2 - 24n + 36}
\][/tex]
