Question

Which equation is true?

9x2 – 25 = (3x – 5)(3x – 5)
9x2 – 25 = (3x – 5)(3x + 5)
9x2 – 25 = –(3x + 5)(3x + 5)
9x2 – 25 = –(3x + 5)(3x – 5)

Answer 1

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

Answer 2

ANSWER


`9 {x}^(2) - 25 = (3x - 5)(3x + 5)`

Step-by-step 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.