To express the product \((x^2 - 9)(x^2 - 16)\) as linear factors, we first recognize that both \(x^2 - 9\) and \(x^2 - 16\) can be factored using the difference of squares formula:
- \(x^2 - 9 = (x - 3)(x + 3)\)
- \(x^2 - 16 = (x - 4)(x + 4)\)
Now, we can substitute these factorizations back into the original expression:
\[ (x^2 - 9)(x^2 - 16) = [(x - 3)(x + 3)][(x - 4)(x + 4)] \]
Next, we can combine all the factors together:
\[ (x - 3)(x + 3)(x - 4)(x + 4) \]
Thus, the complete product expressed as linear factors is:
\[ (x - 3)(x + 3)(x - 4)(x + 4) \]