Multiply the polynomial (b + 8) (3b - 6) to simplify.

b^2 + 18b - 36
b^2 + 30b - 48
3b^2 + 18b - 48
3b^2 + 30b - 48

1 answer

To multiply the polynomial \( (b + 8)(3b - 6) \), we will 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 the like terms:

\[ 3b^2 + ( -6b + 24b ) - 48 = 3b^2 + 18b - 48 \]

Thus, the simplified result is:

\[ \boxed{3b^2 + 18b - 48} \]

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