Which of the following trinomials is equivalent to [tex]$(A-B)^2$[/tex], where [tex]$A=n x$[/tex] and [tex][tex]$B=m$[/tex][/tex], and [tex]$n$[/tex] and [tex]$m$[/tex] are positive integers?

A. [tex]$36 x^2 + 60 x + 25$[/tex]
B. [tex][tex]$36 x^2 + 60 x - 25$[/tex][/tex]
C. [tex]$36 x^2 - 60 x + 25$[/tex]
D. [tex]$36 x^2 - 60 x - 25$[/tex]

To solve this problem, we need to expand the expression [tex]$(A-B)^2$[/tex], where [tex]$A = n \cdot x$[/tex] and [tex]$B = m$[/tex]. We are given specific values [tex]$n = 6$[/tex] and [tex]$m = 5$[/tex]. This means:

- [tex]$A = 6x$[/tex]
- [tex]$B = 5$[/tex]

Now, let's expand the expression [tex]$(A-B)^2$[/tex]:

[tex]\[
(A-B)^2 = (6x - 5)^2
\][/tex]

Using the formula for the square of a binomial, [tex]$(a-b)^2 = a^2 - 2ab + b^2$[/tex], we can expand [tex]$(6x - 5)^2$[/tex]:

1. Calculate [tex]$a^2$[/tex]:
[tex]\[
(6x)^2 = 36x^2
\][/tex]

2. Calculate [tex]$-2ab$[/tex]:
[tex]\[
-2 \cdot (6x) \cdot 5 = -60x
\][/tex]

3. Calculate [tex]$b^2$[/tex]:
[tex]\[
5^2 = 25
\][/tex]

Putting it all together:

[tex]\[
(6x - 5)^2 = 36x^2 - 60x + 25
\][/tex]

Now, compare this expanded expression with the given options:

a) [tex]$36x^2 + 60x + 25$[/tex]

b) [tex]$36x^2 + 60x - 25$[/tex]

c) [tex]$36x^2 - 60x + 25$[/tex]

d) [tex]$36x^2 - 60x - 25$[/tex]

The option that matches the expanded expression [tex]$36x^2 - 60x + 25$[/tex] is option c). Therefore, the trinomial [tex]$36x^2 - 60x + 25$[/tex] is equivalent to [tex]$(A-B)^2$[/tex].