Question

Find the product of (2q9+3q7)(−6q2+9) (1 point) Responses −12q11−36q9+27q7 negative 12 q to the 11th power minus 36 q to the 9th power plus 27 q to the 7th power −12q11+27q7 negative 12 q to the 11th power plus 27 q to the 7th power −12q18+27q7 negative 12 q to the 18th power plus 27 q to the 7th power −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 when dealing with binomials).

Let's distribute each term in the first polynomial \((2q^9 + 3q^7)\) by each term in the second polynomial \((-6q^2 + 9)\):

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

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

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

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

Now we can combine all the products:

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

Next, simplify the terms:

• \(18q^9 - 18q^9 = 0\)

So, we are left with:

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

Thus, the final expression is:

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

Looking at the responses:

• Correct answer is: \(-12q^{11} + 27q^7\)