Question
Find the area of the rectangle below:
3x3
−4x3 +5
(1 point)
Responses
12x6−15x3
12 x to the 6th power minus 15 x cubed
−12x9+15x3
negative 12 x to the 9th power plus 15 x cubed
−12x6+15x3
negative 12 x to the 6th power plus 15 x cubed
−x3+5
negative x cubed plus 5
11x3−2
3x3
−4x3 +5
(1 point)
Responses
12x6−15x3
12 x to the 6th power minus 15 x cubed
−12x9+15x3
negative 12 x to the 9th power plus 15 x cubed
−12x6+15x3
negative 12 x to the 6th power plus 15 x cubed
−x3+5
negative x cubed plus 5
11x3−2
Answers
GPT-4o mini
To find the area of the rectangle given the expressions \(3x^3\) and \(-4x^3 + 5\), we need to multiply these two expressions together:
\[
\text{Area} = (3x^3)(-4x^3 + 5)
\]
Now, we will distribute \(3x^3\) to both terms in the second expression:
\[
\text{Area} = 3x^3 \cdot (-4x^3) + 3x^3 \cdot 5
\]
Calculating each part:
1. \(3x^3 \cdot (-4x^3) = -12x^{3 + 3} = -12x^6\)
2. \(3x^3 \cdot 5 = 15x^3\)
Now combine these results:
\[
\text{Area} = -12x^6 + 15x^3
\]
Thus, the area of the rectangle is:
\[
-12x^6 + 15x^3
\]
From the options provided, the correct response is:
**−12x^6 + 15x^3**.
\[
\text{Area} = (3x^3)(-4x^3 + 5)
\]
Now, we will distribute \(3x^3\) to both terms in the second expression:
\[
\text{Area} = 3x^3 \cdot (-4x^3) + 3x^3 \cdot 5
\]
Calculating each part:
1. \(3x^3 \cdot (-4x^3) = -12x^{3 + 3} = -12x^6\)
2. \(3x^3 \cdot 5 = 15x^3\)
Now combine these results:
\[
\text{Area} = -12x^6 + 15x^3
\]
Thus, the area of the rectangle is:
\[
-12x^6 + 15x^3
\]
From the options provided, the correct response is:
**−12x^6 + 15x^3**.