1. **State the problem:** Factor the expression $2n^2 - 8$. 2. **Recall the formula and rules:** We use the distributive property and factoring out the greatest common factor (GCF). The GCF is the largest factor common to all terms. 3. **Find the GCF:** The terms are $2n^2$ and $-8$. The GCF of 2 and 8 is 2. 4. **Factor out the GCF:** $$2n^2 - 8 = 2(n^2 - 4)$$ 5. **Recognize the difference of squares:** $n^2 - 4$ is a difference of squares since $4 = 2^2$. 6. **Apply the difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$ Here, $a = n$ and $b = 2$. 7. **Factor the difference of squares:** $$n^2 - 4 = (n - 2)(n + 2)$$ 8. **Write the fully factored form:** $$2n^2 - 8 = 2(n - 2)(n + 2)$$ **Final answer:** $2(n - 2)(n + 2)$