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 defined by the given dimensions, we need to multiply the two expressions provided for the lengths of the sides. The dimensions given are \(3x^3\) and \(-4x^3 + 5\).
The area \(A\) of the rectangle is calculated as follows:
\[
A = (3x^3) \times (-4x^3 + 5)
\]
Now, we distribute \(3x^3\) across the binomial \(-4x^3 + 5\):
1. **Multiply \(3x^3\) by \(-4x^3\)**:
\[
3x^3 \times -4x^3 = -12x^{3+3} = -12x^6
\]
2. **Multiply \(3x^3\) by \(5\)**:
\[
3x^3 \times 5 = 15x^3
\]
Now, we combine these results:
\[
A = -12x^6 + 15x^3
\]
Thus, the area of the rectangle is:
\[
\text{Area} = -12x^6 + 15x^3
\]
The correct response from the options provided is:
**−12x^6 + 15x^3**
The area \(A\) of the rectangle is calculated as follows:
\[
A = (3x^3) \times (-4x^3 + 5)
\]
Now, we distribute \(3x^3\) across the binomial \(-4x^3 + 5\):
1. **Multiply \(3x^3\) by \(-4x^3\)**:
\[
3x^3 \times -4x^3 = -12x^{3+3} = -12x^6
\]
2. **Multiply \(3x^3\) by \(5\)**:
\[
3x^3 \times 5 = 15x^3
\]
Now, we combine these results:
\[
A = -12x^6 + 15x^3
\]
Thus, the area of the rectangle is:
\[
\text{Area} = -12x^6 + 15x^3
\]
The correct response from the options provided is:
**−12x^6 + 15x^3**