Find the product of

To find the product of \( (2p^9 + 3p^7)(-6p^2 + 9) \), we can use the distributive property (also known as the FOIL method in the context of binomials).

We will distribute each term in the first polynomial to each term in the second polynomial:

1. Distributing \( 2p^9 \):

   • \( 2p^9 \cdot (-6p^2) = -12p^{11} \)
   • \( 2p^9 \cdot 9 = 18p^9 \)

2. Distributing \( 3p^7 \):

   • \( 3p^7 \cdot (-6p^2) = -18p^{9} \)
   • \( 3p^7 \cdot 9 = 27p^7 \)

Now we combine all these products:

\[ -12p^{11} + 18p^9 - 18p^9 + 27p^7 \]

Next, we combine like terms:

• The \( p^9 \) terms: \( 18p^9 - 18p^9 = 0 \)

Thus, we are left with:

\[ -12p^{11} + 27p^7 \]

This expression can be simplified to:

\[ -12p^{11} + 27p^7 \]

Now we can check against the provided options:

A: \(-12p^{11} - 36p^{9} + 27p^7\) (not our answer)

B: \(-12p^{18} + 27p^7\) (not our answer)

C: \(-12p^{11} + 36p^{9} + 27p^7\) (not our answer)

D: \(-12p^{11} + 27p^7\) (this matches our answer)

Thus, the correct answer is:

\[ \boxed{D} \]