Question

Which equation is true?

Answer 1

That would be (9x2 - 25 = (3x-5) (3x+5)

Answer 2

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.