Final answer:
To multiply a polynomial by a monomial, distribute the monomial across each term of the polynomial and combine like terms. For the expression -v(-3v²-3v), the result is 3v³ + 3v² after applying the distributive property and simplifying the expression.
Step-by-step explanation:
The student is asking to multiply a polynomial by a monomial. The given expression is -v(-3v²-3v). To find the product and simplify the expression, we apply the distributive property which involves multiplying the monomial -v by each term in the polynomial (-3v²-3v).
First, we multiply -v by -3v²:
-v * -3v² = 3v³ (since the negative sign times a negative sign gives a positive, and we add exponents when multiplying like bases).
Then, we multiply -v by -3v:
-v * -3v = 3v² (the negative signs cancel out here as well).
Therefore, the simplified result is:
3v³ + 3v²