1. **State the problem:** Factor the quadratic expression $w^2 + 10w + 16$ completely. 2. **Recall the factoring formula:** For a quadratic $w^2 + bw + c$, we look for two numbers that multiply to $c$ and add to $b$. 3. **Identify $b$ and $c$:** Here, $b = 10$ and $c = 16$. 4. **Find two numbers that multiply to 16 and add to 10:** These numbers are 8 and 2 because $8 \times 2 = 16$ and $8 + 2 = 10$. 5. **Write the factored form:** $$w^2 + 10w + 16 = (w + 8)(w + 2)$$ 6. **Verify by expansion:** $$(w + 8)(w + 2) = w^2 + 2w + 8w + 16 = w^2 + 10w + 16$$ This confirms the factorization is correct. **Final answer:** $$\boxed{(w + 8)(w + 2)}$$