1. **State the problem:** Factor the expression $4x^2 - 16$. 2. **Formula and rules:** To factor expressions like this, look for the greatest common factor (GCF) and recognize special products such as the difference of squares. 3. **Find the GCF:** Both terms $4x^2$ and $16$ have a common factor of $4$. 4. **Factor out the GCF:** $$4x^2 - 16 = 4(x^2 - 4)$$ 5. **Recognize difference of squares:** $$x^2 - 4 = (x)^2 - (2)^2$$ 6. **Apply difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ 7. **Factor the expression inside the parentheses:** $$x^2 - 4 = (x - 2)(x + 2)$$ 8. **Write the fully factored form:** $$4x^2 - 16 = 4(x - 2)(x + 2)$$ **Final answer:** $4(x - 2)(x + 2)$