Find the product of (2q9+3q7)(−6q2+9)

Question

.(1 point)
Responses

−12q18+27q7
negative 12 q superscript 18 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

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

−12q11+27q7

Answer 1

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

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

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

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

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

Now we combine all the terms: \[ -12q^{11} + 18q^9 - 18q^9 + 27q^7 \]

The \(18q^9\) and \(-18q^9\) cancel each other out: \[ -12q^{11} + 27q^{7} \]

Thus, the final product is: \[ -12q^{11} + 27q^{7} \]

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