1. **State the problem:** Factor the expression $x^4 - 16$. 2. **Recall the formula:** This is a difference of squares since $x^4 = (x^2)^2$ and $16 = 4^2$. 3. **Apply difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ Here, $a = x^2$ and $b = 4$, so $$x^4 - 16 = (x^2 - 4)(x^2 + 4)$$ 4. **Factor further:** Notice $x^2 - 4$ is also a difference of squares: $$x^2 - 4 = (x - 2)(x + 2)$$ 5. **Final factorization:** $$x^4 - 16 = (x - 2)(x + 2)(x^2 + 4)$$ 6. **Explanation:** We used the difference of squares formula twice to break down the original polynomial into simpler factors. The term $x^2 + 4$ cannot be factored further over the real numbers. **Answer:** $$x^4 - 16 = (x - 2)(x + 2)(x^2 + 4)$$