Final answer:
To simplify the expression -7v⁵ (4v³-7v²+5v), distribute -7v⁵ across each term within the parentheses, resulting in -28v⁸ + 49v⁷ - 35v⁶. Then check to ensure the exponents have been correctly added and the distribution is properly applied.
Step-by-step explanation:
To rewrite the expression -7v⁵ (4v³-7v²+5v) without parentheses and simplify it, we need to distribute the -7v⁵ across each term inside the parentheses:
- Multiply -7v⁵ by 4v³ to get -28v⁸ (because 5 + 3 = 8).
- Multiply -7v⁵ by -7v² to get +49v⁷ (5 + 2 = 7).
- Multiply -7v⁵ by 5v to get -35v⁶ (5 + 1 = 6).
So, the expanded and simplified form of the expression is -28v⁸ + 49v⁷ - 35v⁶.
We should always check the answer to see if it is reasonable, which in this case, involves confirming that the powers are correctly added and the distribution is properly applied.