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:
- \( 3x^3 \cdot (-4x^3) = -12x^{6} \)
- \( 3x^3 \cdot 5 = 15x^3 \)
Combining both terms gives:
\[ A = -12x^6 + 15x^3 \]
Thus, the area of the rectangle is:
\[ A = -12x^6 + 15x^3 \]