Simplify the following expression by factoring.  Identify the factors below that would leave your answer in the simplest factored form. 81a4 - 16b4

The given expression is 81a^4 - 16b^4.

Step 1: Recognize that this is a difference of squares, which can be factored as (A^2 - B^2) = (A - B)(A + B). Here, A = 9a^2 and B = 4b^2.

Step 2: Substitute A and B into the difference of squares formula. This gives us (9a^2 - 4b^2)(9a^2 + 4b^2).

Step 3: Notice that the first term in the product is also a difference of squares. We can factor it further using the same formula. Here, A = 3a and B = 2b.

Step 4: Substitute A and B into the difference of squares formula. This gives us (3a - 2b)(3a + 2b)(9a^2 + 4b^2).

So, the simplest factored form of the expression 81a^4 - 16b^4 is (3a - 2b)(3a + 2b)(9a^2 + 4b^2).