Multiply the polynomial (b+8)(3b−6) to simplify.(1 point) Responses b2+30b−48 b squared plus 30 b minus 48 3b2+30b−48 3 b squared plus 30 b minus 48 3b2+18b−48 3 b squared plus 18 b minus 48 b2+18b−36

Answer 1

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

1. Distribute \(b\) to both terms in the second polynomial:

   • \(b \cdot 3b = 3b^2\)
   • \(b \cdot (-6) = -6b\)

2. Distribute \(8\) to both terms in the second polynomial:

   • \(8 \cdot 3b = 24b\)
   • \(8 \cdot (-6) = -48\)

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

Next, combine like terms:

• The \(b\) terms: \(-6b + 24b = 18b\)

Putting it all together gives: \[ 3b^2 + 18b - 48 \]

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

This corresponds with the option "3b^2 + 18b - 48".