ANSWER
[tex]9 {x}^{2} - 25 = (3x - 5)(3x + 5)[/tex]
EXPLANATION
We want to factor
[tex]9 {x}^{2} - 25[/tex]
Observe that, both
[tex]9[/tex] and [tex]25[/tex] are perfect squares.
Thus,
[tex]9 {x}^{2} = {3}^{2} {x}^{2} = {(3x)}^{2} [/tex]
and
[tex]25 = {5}^{2} [/tex]
We need to rewrite the expression as a difference of two squares to obtain,
[tex]9 {x}^{2} - 25 = (3x)^{2} - {5}^{2} [/tex]
We apply the difference of two squares formula which is given by,
[tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex]
By comparing this to our expression we let
[tex]a = 3x \: \: and \: \: b = 5[/tex]
Then our expression can now be factored as,
[tex]9 {x}^{2} - 25 = (3x - 5)(3x + 5)[/tex]
Therefore the correct option is B.
