Realize that [tex]25x^2 - 81[/tex] is the difference of two squares, [tex]25x^2[/tex] and 81. This means that we can use the formula for the difference of two squares, which is:
[tex]a^2 - b^2 = (a + b)(a - b)[/tex]
In this case, we can say [tex]a^2 = 25x^2[/tex] and [tex]b^2 = 81[/tex]. Taking the square root of both sides of the equations means that we will get the following:
[tex]\sqrt{a^2} = \sqrt{25x^2} \Rightarrow a = 5x[/tex]
[tex]\sqrt{b^2} = \sqrt{81} \Rightarrow b = 9[/tex]
Using our formula for the difference of squares, we get:
[tex]25x^2 - 81 = \boxed{(5x - 9)(5x + 9)}[/tex]
Thus, the answer would be Choice C, or (5x + 9)(5x - 9).
