Find the product. Simplify your answer. (q + 3)(-3q^2 + 3q + 3) ______

Multiply by q: We multiply q by each term in the second polynomial: q * (-3q^2), q * (3q), and q * (3). This gives us: -3q^3, 3q^2, and 3q.Multiply by 3: Next, we multiply 3 by each term in the second polynomial: 3 * (-3q^2), 3 * (3q), and 3 * (3). This gives us: -9q^2, 9q, and 9.Combine like terms: Now, we combine the like terms from the two sets of products. The combined terms are: -3q^3 from the first set, and -9q^2 + 3q^2 from the second set, which simplifies to -6q^2. Then we have 3q + 9q, which simplifies to 12q. Lastly, we have the constant term 9.Final simplified form: The final simplified form of the product is the sum of all these terms: -3q^3 - 6q^2 + 12q + 9.

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Find the product. Simplify your answer. $\newline$ $(q + 3)(-3q^2 + 3q + 3)$

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Q. Find the product. Simplify your answer.

\newline

(q + 3)(-3q^2 + 3q + 3)

Multiply by $q$ : We multiply $q$ by each term in the second polynomial: $q \times (-3q^2)$ , $q \times (3q)$ , and $q \times (3)$ . This gives us: $-3q^3$ , $3q^2$ , and $3q$ .
Multiply by $3$ : Next, we multiply $3$ by each term in the second polynomial: $3 \times (-3q^2)$ , $3 \times (3q)$ , and $3 \times (3)$ . This gives us: $-9q^2$ , $9q$ , and $9$ .
Combine like terms: Now, we combine the like terms from the two sets of products. The combined terms are: $-3q^3$ from the first set, and $-9q^2 + 3q^2$ from the second set, which simplifies to $-6q^2$ . Then we have $3q + 9q$ , which simplifies to $12q$ . Lastly, we have the constant term $9$ .
Final simplified form: The final simplified form of the product is the sum of all these terms: $-3q^3 - 6q^2 + 12q + 9$ .