Question
what is the area of a rectangle if the width is 3x^3 and the length is -4x^3 + 5
Answers
GPT-4o mini
To find the area of a rectangle, you multiply the width by the length. Given that the width is \( 3x^3 \) and the length is \( -4x^3 + 5 \), we can calculate the area \( A \) as follows:
\[
A = \text{width} \times \text{length} = (3x^3)(-4x^3 + 5)
\]
Now, we can distribute the \( 3x^3 \):
\[
A = 3x^3 \cdot (-4x^3) + 3x^3 \cdot 5
\]
Calculating each term separately:
1. \( 3x^3 \cdot (-4x^3) = -12x^{6} \)
2. \( 3x^3 \cdot 5 = 15x^3 \)
Combining both terms gives:
\[
A = -12x^6 + 15x^3
\]
Thus, the area of the rectangle is:
\[
A = -12x^6 + 15x^3
\]
\[
A = \text{width} \times \text{length} = (3x^3)(-4x^3 + 5)
\]
Now, we can distribute the \( 3x^3 \):
\[
A = 3x^3 \cdot (-4x^3) + 3x^3 \cdot 5
\]
Calculating each term separately:
1. \( 3x^3 \cdot (-4x^3) = -12x^{6} \)
2. \( 3x^3 \cdot 5 = 15x^3 \)
Combining both terms gives:
\[
A = -12x^6 + 15x^3
\]
Thus, the area of the rectangle is:
\[
A = -12x^6 + 15x^3
\]