Find the product. Simplify your answer. -6(-q^2 + 9)
Understand the Problem
The question is asking for the product of the expression -6(-q^2 + 9) and to simplify the answer. This involves applying the distributive property to simplify the expression.
Answer
The product is $6q^2 - 54$.
Answer for screen readers
The simplified product is $6q^2 - 54$.
Steps to Solve
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Apply the Distributive Property
To find the product of the expression, we use the distributive property. This means we multiply -6 by each term inside the parentheses: $$ -6 \cdot (-q^2) + -6 \cdot 9 $$
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Multiply Each Term
Calculate the product for each term:
- First term: $$ -6 \cdot (-q^2) = 6q^2 $$
- Second term: $$ -6 \cdot 9 = -54 $$
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Combine the Results
Now we can write down the simplified expression by combining the results from the multiplication: $$ 6q^2 - 54 $$
The simplified product is $6q^2 - 54$.
More Information
This expression can further be factored, but as it stands, it is simplified. The factoring process involves recognizing the common factor of 6 in the terms.
Tips
- Forgetting to distribute the negative sign can lead to incorrect signs in the resulting expression.
- Not collecting like terms after distribution might lead to incomplete simplification.
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