To multiply the polynomial \((b+8)(3b-6)\), we can use the distributive property (also known as the FOIL method for binomials).
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Distribute \(b\) to both terms in \(3b - 6\):
- \(b \cdot 3b = 3b^2\)
- \(b \cdot (-6) = -6b\)
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Distribute \(8\) to both terms in \(3b - 6\):
- \(8 \cdot 3b = 24b\)
- \(8 \cdot (-6) = -48\)
Now, combine all the terms: \[ 3b^2 - 6b + 24b - 48 \] Combine like terms \(-6b\) and \(24b\): \[ 3b^2 + 18b - 48 \]
So, the simplified multiplication of \((b+8)(3b-6)\) is: \[ 3b^2 + 18b - 48 \]
The correct response is: 3b² + 18b - 48.