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: $$\boxed{{\displaystyle 3b^2+18b-48}}$$

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