I'm trying to factor this and I just can't figure it out. Help?
r^4 s^4 - 81
difference of two squares
r^4 s^4 - 81
(r^2s^2 - 9 )(r^2s^2 + 9 )
(rs-3)(rs+3)(r^2s^2+9)
To factor the expression r^4 s^4 - 81, we can use the difference of squares formula. The difference of squares formula states that a^2 - b^2 can be written as (a + b)(a - b).
In our case, r^4 s^4 - 81 can be seen as (r^2 s^2)^2 - 9^2. Applying the difference of squares formula, we have:
(r^2 s^2 + 9)(r^2 s^2 - 9)
Now, let's go over the steps to reach this result:
1. Recognize that the expression r^4 s^4 - 81 is a difference of squares, where r^4 s^4 is the square of (r^2 s^2) and 81 is the square of 9.
2. Apply the difference of squares formula: (a^2 - b^2) can be factored as (a + b)(a - b).
3. Substitute r^2 s^2 for a and 9 for b to get (r^2 s^2 + 9)(r^2 s^2 - 9).
So, the factored form of r^4 s^4 - 81 is (r^2 s^2 + 9)(r^2 s^2 - 9).