Question

Factor completely 9x2 − 25.

A. (3x + 5)(3x − 5)
B. (3x − 5)(3x − 5)
C. (9x + 5)(x − 5)
D. (9x − 5)(x + 5)

Answer 1

the answer to the equation is A

Answer 2

To solve this we are going to use the difference of squares formula:
`a^2-b^2=(a+b)(a-b)`.

Notice that the first term of our binomial
`9x^2` can be expressed as
`(3x)^2`; similarly, the second term
`25` can be expressed as
`5^2`. So we can rewrite our binomial as follows:

`9x^2-25=(3x)^2-5^2`
Now we have a difference of squares with
`a=3x` and
`b=5`, so lets apply our formula:

`(3x)^2-5^2=(3x+5)(3x-5)`

We can conclude that the correct answer is A. (3x + 5)(3x − 5)