1. **State the problem:** Simplify the expression $-4\sqrt{100} + 10\sqrt{16}$. 2. **Recall the square root values:** - $\sqrt{100} = 10$ - $\sqrt{16} = 4$ 3. **Substitute these values into the expression:** $$-4\sqrt{100} + 10\sqrt{16} = -4 \times 10 + 10 \times 4$$ 4. **Perform the multiplications:** $$-4 \times 10 = -40$$ $$10 \times 4 = 40$$ 5. **Add the results:** $$-40 + 40 = 0$$ 6. **Final answer:** $$0$$