Question: -7w^2(-3w^3+4w)
Simplify your answer as much as possible.
1. **State the problem:** Simplify the expression $$-7w^2(-3w^3+4w)$$.
2. **Recall the distributive property:** To simplify, multiply $$-7w^2$$ by each term inside the parentheses.
3. **Multiply the first term:** $$-7w^2 \times -3w^3 = (-7 \times -3)(w^2 \times w^3) = 21w^{2+3} = 21w^5$$.
4. **Multiply the second term:** $$-7w^2 \times 4w = (-7 \times 4)(w^2 \times w) = -28w^{2+1} = -28w^3$$.
5. **Combine the results:** $$21w^5 - 28w^3$$.
6. **Factor if possible:** Factor out the common term $$7w^3$$:
$$21w^5 - 28w^3 = 7w^3(3w^2 - 4)$$.
**Final simplified expression:** $$7w^3(3w^2 - 4)$$.