Find the product of (2q9+3q7)(−6q2+9)

Question

.(1 point)
Responses

−12q11+27q7
negative 12 q superscript 11 baseline plus 27 q superscript 7 baseline

−12q11+36q9+27q7
negative 12 q superscript 11 baseline plus 36 q superscript 9 baseline plus 27 q superscript 7 baseline

−12q18+27q7
negative 12 q superscript 18 baseline plus 27 q superscript 7 baseline

−12q11−36q9+27q7

Answer 1

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

Let's distribute each term in the first polynomial by each term in the second polynomial:

1. First term \(2q^9\) multiplied by both terms in \(-6q^2 + 9\):

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

2. Second term \(3q^7\) multiplied by both terms in \(-6q^2 + 9\):

   • \(3q^7 \cdot (-6q^2) = -18q^9\)
   • \(3q^7 \cdot 9 = 27q^7\)

Now, we can combine all these results:

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

Now, notice that \(18q^9 - 18q^9 = 0\). So, we can simplify:

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

Therefore, the final answer is:

\(-12q^{11} + 27q^{7}\)

So, the correct response is: \(-12q^{11} + 27q^{7}\)