Find the product of (2q6+3q7)(−6q2+9)
(1 point)
Responses
−12q11+27q7
negative 12 q to the 11th 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
−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 plus 36 q to the 9th power plus 27 q to the 7th power
The correct response is:
−12q11−36q9+27q7
To find the product of (2q^6+3q^7)(-6q^2+9), we need to apply the distributive property and multiply each term of the first expression by each term of the second expression.
Step 1: Multiply the first term of the first expression (2q^6) by both terms of the second expression (-6q^2 and 9):
(2q^6)(-6q^2) = -12q^8
(2q^6)(9) = 18q^6
Step 2: Multiply the second term of the first expression (3q^7) by both terms of the second expression (-6q^2 and 9):
(3q^7)(-6q^2) = -18q^9
(3q^7)(9) = 27q^7
Step 3: Combine the like terms:
-12q^8 + 18q^6 - 18q^9 + 27q^7
Thus, the product of (2q^6+3q^7)(-6q^2+9) is -12q^8 + 18q^6 - 18q^9 + 27q^7.
To find the product of (2q^6 + 3q^7)(-6q^2 + 9), you need to multiply each term in the first expression by each term in the second expression. Here's how you can do it step by step:
Step 1: Multiply the first term in the first expression (2q^6) by each term in the second expression (-6q^2 + 9):
-6q^2 * 2q^6 = -12q^8
9 * 2q^6 = 18q^6
Step 2: Multiply the second term in the first expression (3q^7) by each term in the second expression (-6q^2 + 9):
-6q^2 * 3q^7 = -18q^9
9 * 3q^7 = 27q^7
Step 3: Combine like terms:
-12q^8 + 18q^6 - 18q^9 + 27q^7
Therefore, the correct answer is -12q^8 + 18q^6 - 18q^9 + 27q^7.