1. **State the problem:** Simplify the expression $2x^2 - 8$. 2. **Identify the formula and rules:** We can factor out the greatest common factor (GCF) from the terms. 3. **Find the GCF:** The GCF of $2x^2$ and $8$ is $2$. 4. **Factor out the GCF:** $$2x^2 - 8 = 2(x^2 - 4)$$ 5. **Recognize the difference of squares:** $$x^2 - 4 = (x - 2)(x + 2)$$ 6. **Write the fully factored form:** $$2(x - 2)(x + 2)$$ **Final answer:** $$2(x - 2)(x + 2)$$