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