Simplify the following expression.

Question

(3p+6)(6p2−8p−1)


(1 point)
Responses

18p3+12p2−51p−6
18 p cubed plus 12 p squared minus 51 p minus 6

40p3−33p2−23p+6
40 p cubed minus 33 p squared minus 23 p plus 6

28p3+23p2−3p+15
28 p cubed plus 23 p squared minus 3 p plus 15

−3p3−20p2+p−42
negative 3 p cubed minus 20 p squared plus p minus 42
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Answer 1

To simplify the expression \((3p+6)(6p^2−8p−1)\), we will use the distributive property (also known as the FOIL method for binomials).

1. Distribute \(3p\) to each term in the second polynomial:

   \[ 3p \cdot 6p^2 = 18p^3 \] \[ 3p \cdot (-8p) = -24p^2 \] \[ 3p \cdot (-1) = -3p \]

2. Distribute \(6\) to each term in the second polynomial:

   \[ 6 \cdot 6p^2 = 36p^2 \] \[ 6 \cdot (-8p) = -48p \] \[ 6 \cdot (-1) = -6 \]

3. Combine all these results:

   Now, we add all the results together:

   \[ 18p^3 + (-24p^2 + 36p^2) + (-3p - 48p) - 6 \]

   Combine like terms:

   • For \(p^2\): \(-24p^2 + 36p^2 = 12p^2\)
   • For \(p\): \(-3p - 48p = -51p\)

   So we have:

   \[ 18p^3 + 12p^2 - 51p - 6 \]

The simplified result of the expression \((3p+6)(6p^2−8p−1)\) is:

\[ \boxed{18p^3 + 12p^2 - 51p - 6} \]