How do I factor 9x^2 - 49?
I believe this is a difference of squares, but I'm not sure how to do it with the 9 in front of the first term.......
(3x)^2-7^2
(3x-7)(3x+7)
To factor the expression 9x^2 - 49, you are correct that it can be written as a difference of squares. The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b).
In this specific case, you have 9x^2 - 49. To use the difference of squares formula, you need to rewrite each term as a perfect square.
First, write 9x^2 as (3x)^2, since (3x)(3x) = 9x^2. Similarly, write 49 as (7)^2, since (7)(7) = 49.
Now the expression becomes (3x)^2 - (7)^2.
Using the difference of squares formula, you can factor it as (3x + 7)(3x - 7).
So, the factored form of 9x^2 - 49 is (3x + 7)(3x - 7).