Let's simplify the expression [tex]\((3n - 2m)^2\)[/tex] step-by-step.
First, recall the algebraic identity for the square of a binomial:
[tex]\[
(a - b)^2 = a^2 - 2ab + b^2
\][/tex]
In this case, we can identify [tex]\(a\)[/tex] and [tex]\(b\)[/tex] as follows:
[tex]\[
a = 3n \quad \text{and} \quad b = 2m
\][/tex]
Now, applying the identity to our expression:
[tex]\[
(3n - 2m)^2 = (3n)^2 - 2(3n)(2m) + (2m)^2
\][/tex]
Let's calculate each term individually:
1. [tex]\( (3n)^2 = 9n^2 \)[/tex]
2. [tex]\( -2(3n)(2m) = -12mn \)[/tex]
3. [tex]\( (2m)^2 = 4m^2 \)[/tex]
Now, combining these terms together, we get:
[tex]\[
(3n - 2m)^2 = 9n^2 - 12mn + 4m^2
\][/tex]
Therefore, the simplified form of [tex]\((3n - 2m)^2\)[/tex] is:
[tex]\[
9n^2 - 12mn + 4m^2
\][/tex]
Comparing this result with the given option, we see that the correct answer is:
D. [tex]\(9 n^2 - 12 m n + 4 m^2\)[/tex]
