Multiplying Polynomials Quick Check 1 of 51 of 5 Items Question Multiply the polynomial (b+8)(3b−6) to simplify.(1 point) Responses b2+30b−48 b squared plus 30 b minus 48 b2+18b−36 b squared plus 18 b minus 36 3b2+18b−48 3 b squared plus 18 b minus 48 3b2+30b−48

Answer 1

To multiply the polynomial \((b + 8)(3b - 6)\), we can use the distributive property (also known as the FOIL method for binomials).

1. First: Multiply the first terms: \[ b \cdot 3b = 3b^2 \]

2. Outer: Multiply the outer terms: \[ b \cdot (-6) = -6b \]

3. Inner: Multiply the inner terms: \[ 8 \cdot 3b = 24b \]

4. Last: Multiply the last terms: \[ 8 \cdot (-6) = -48 \]

Now, combine all these results: \[ 3b^2 - 6b + 24b - 48 \]

Combine like terms: \[ 3b^2 + 18b - 48 \]

So, the simplified form of \((b + 8)(3b - 6)\) is: \[ \boxed{3b^2 + 18b - 48} \]

Thus, the correct response is 3b² + 18b − 48.