Question: Rewrite without parentheses.
$-8u^3(7u^3 - 2u^2 + 4u)$
Simplify your answer as much as possible.
1. **State the problem:**
Rewrite the expression $$-8u^3(7u^3 - 2u^2 + 4u)$$ without parentheses and simplify it as much as possible.
2. **Formula and rules:**
Use the distributive property: $$a(b + c + d) = ab + ac + ad$$.
When multiplying powers with the same base, add the exponents: $$u^m \times u^n = u^{m+n}$$.
3. **Apply the distributive property:**
$$-8u^3 \times 7u^3 = -8 \times 7 \times u^{3+3} = -56u^6$$
$$-8u^3 \times (-2u^2) = -8 \times (-2) \times u^{3+2} = 16u^5$$
$$-8u^3 \times 4u = -8 \times 4 \times u^{3+1} = -32u^4$$
4. **Combine all terms:**
$$-56u^6 + 16u^5 - 32u^4$$
5. **Final simplified expression:**
$$\boxed{-56u^6 + 16u^5 - 32u^4}$$