Find the product of (2q9+3q7)(−6q2+9)

Question

(1 point)
Responses

−12q18+27q7
negative 12 q to the 18th power plus 27 q to the 7th power

−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+36q9+27q7
negative 12 q to the 11th power plus 36 q to the 9th power plus 27 q to the 7th power

−12q11+27q7

Answer 1

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

1. Distribute \(2q^9\) to both terms in the second factor:

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

2. Distribute \(3q^7\) to both terms in the second factor:

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

3. Now, add all these results together: \[ -12q^{11} + 18q^9 - 18q^9 + 27q^7 \]

4. Combine like terms: \[ -12q^{11} + (18q^9 - 18q^9) + 27q^7 = -12q^{11} + 0 + 27q^7 = -12q^{11} + 27q^7 \]

The final result is: \[ -12q^{11} + 27q^7 \]

The correct response is: −12q11+27q7