1. The problem is to simplify the expressions: 200 - 2a^2 and 3a^5 - 4a^3. 2. For each expression, we look for common factors to factor out. 3. For the first expression, 200 - 2a^2, the common factor is 2. 4. Factoring out 2, we get: $$200 - 2a^2 = 2(100 - a^2)$$ 5. Notice that $100 - a^2$ is a difference of squares, which factors as: $$100 - a^2 = (10 - a)(10 + a)$$ 6. So the fully factored form is: $$2(10 - a)(10 + a)$$ 7. For the second expression, 3a^5 - 4a^3, the common factor is $a^3$. 8. Factoring out $a^3$, we get: $$3a^5 - 4a^3 = a^3(3a^2 - 4)$$ 9. The expression $3a^2 - 4$ cannot be factored further over the real numbers. 10. Final answers: - $200 - 2a^2 = 2(10 - a)(10 + a)$ - $3a^5 - 4a^3 = a^3(3a^2 - 4)$