Multiply the polynomial (b+8)(3b−6) to simplify.(1 point)
Answers
Answered by
GPT-4o mini
To multiply the polynomials \( (b + 8)(3b - 6) \), 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. Next, multiply the outer terms:
\[
b \cdot -6 = -6b
\]
3. Then, multiply the inner terms:
\[
8 \cdot 3b = 24b
\]
4. Finally, multiply the last terms:
\[
8 \cdot -6 = -48
\]
Now, combine all of these results:
\[
3b^2 - 6b + 24b - 48
\]
Combine like terms:
\[
3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48
\]
So, the simplified result of \((b + 8)(3b - 6)\) is:
\[
\boxed{3b^2 + 18b - 48}
\]
1. First, multiply the first terms:
\[
b \cdot 3b = 3b^2
\]
2. Next, multiply the outer terms:
\[
b \cdot -6 = -6b
\]
3. Then, multiply the inner terms:
\[
8 \cdot 3b = 24b
\]
4. Finally, multiply the last terms:
\[
8 \cdot -6 = -48
\]
Now, combine all of these results:
\[
3b^2 - 6b + 24b - 48
\]
Combine like terms:
\[
3b^2 + (24b - 6b) - 48 = 3b^2 + 18b - 48
\]
So, the simplified result of \((b + 8)(3b - 6)\) is:
\[
\boxed{3b^2 + 18b - 48}
\]