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

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

We will 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 will combine all these results: \[ -12q^{11} + 18q^9 - 18q^9 + 27q^7 \]

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

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

Among the given options, the correct response is: −12q^(11) + 27q^(7).