Final answer:
The simplified expression of -4u³-8u³+9u²-5u is -12u³ + 9u² - 5u, achieved by combining like terms.
Step-by-step explanation:
To simplify the algebraic expression -4u³-8u³+9u²-5u, we need to combine like terms. The terms -4u³ and -8u³ are like terms because they both contain the variable u raised to the power of 3. Adding these terms together gives us -12u³. The other terms, 9u² and -5u, do not have like terms to combine with. Therefore, the simplified expression is -12u³ + 9u² - 5u.
It is always useful to eliminate terms wherever possible to simplify the algebra and to check the answer to ensure its reasonableness. In this case, the simplification is straightforward, and the answer is reasonable since all like terms have been combined correctly.