Find the product of (2q9+3q7)(−6q2+9)

Question

(
2
𝑞
9
+
3
𝑞
7
)
(
−
6
𝑞
2
+
9
)
.(1 point)
Responses

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

−12q11+27q7
−
12
𝑞
11
+
27
𝑞
7
negative 12 q to the 11th power plus 27 q to the 7th power

−12q11+36q9+27q7
−
12
𝑞
11
+
36
𝑞
9
+
27
𝑞
7
negative 12 q to the 11th power plus 36 q to the 9th power plus 27 q to the 7th power

−12q11−36q9+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). We will multiply each term in the first expression by each term in the second expression.

1. Multiply \(2q^9\) by each term in \(-6q^2 + 9\):

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

2. Multiply \(3q^7\) by each term in \(-6q^2 + 9\):

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

3. Add all the products together: \[ -12q^{11} + 18q^9 - 18q^9 + 27q^7 \]

4. Combine like terms:

   • Notice that \(18q^9\) and \(-18q^9\) cancel each other out.
   • So the expression simplifies to: \[ -12q^{11} + 27q^7 \]

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