3(-3b^2 - b + 2)
Understand the Problem
The question involves multiplying a term with a polynomial and simplifying the expression. The goal is to perform the multiplication and simplify the result.
Answer
The simplified expression is $-9b^2 - 3b + 6$.
Answer for screen readers
The simplified expression is $-9b^2 - 3b + 6$.
Steps to Solve
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Distribute the 3 to each term in the polynomial Multiply 3 by each term in the polynomial $(-3b^2 - b + 2)$.
[ 3 \cdot (-3b^2) + 3 \cdot (-b) + 3 \cdot 2 ]
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Calculate each multiplication Perform the multiplications separately:
- For the first term: [ 3 \cdot (-3b^2) = -9b^2 ]
- For the second term: [ 3 \cdot (-b) = -3b ]
- For the last term: [ 3 \cdot 2 = 6 ]
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Combine the results Now, combine the results from the multiplications:
[ -9b^2 - 3b + 6 ]
The simplified expression is $-9b^2 - 3b + 6$.
More Information
This expression results from multiplying a constant by a polynomial, a common operation in algebra. The distributive property is essential for simplifying such expressions.
Tips
- Forgetting to distribute the constant to all terms in the polynomial, which can lead to incomplete answers.
- Mixing up signs during multiplication, particularly with negative coefficients. Always double-check your signs.
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