Find the product. Simplify your answer. -3v²(-2v² + 3v)
Understand the Problem
The question is asking to find the product of a given expression and then simplify the result. This involves performing multiplication and simplifying algebraic terms.
Answer
The simplified product is $6v^{4} - 9v^{3}$.
Answer for screen readers
The simplified expression is $6v^{4} - 9v^{3}$.
Steps to Solve
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Distribute the expression We need to distribute $-3v^2$ to each term inside the parentheses, $(-2v^2 + 3v)$.
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Apply the multiplication We multiply $-3v^2$ by $-2v^2$: $$ -3v^2 \cdot -2v^2 = 6v^{4} $$
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Multiply the next term Next, multiply $-3v^2$ by $3v$: $$ -3v^2 \cdot 3v = -9v^{3} $$
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Combine the results Now, we combine the results from the multiplications: $$ 6v^{4} - 9v^{3} $$
The simplified expression is $6v^{4} - 9v^{3}$.
More Information
This problem involves algebraic multiplication and is common in polynomial expressions. Distributing terms is a fundamental skill in algebra that helps in simplifying expressions.
Tips
- Forgetting to distribute the negative sign can lead to incorrect signs in the final answer.
- Failing to combine like terms, if applicable, can also result in a more complex answer than needed.
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