To find the area of the rectangle determined by the expressions \(3x^3\) and \(-4x^3 + 5\), we will multiply these two polynomials.
The area \(A\) of the rectangle is given by:
\[ A = (3x^3)(-4x^3 + 5) \]
Now, we distribute \(3x^3\) to each term in \(-4x^3 + 5\):
\[ A = 3x^3 \cdot (-4x^3) + 3x^3 \cdot 5 \]
Calculating each term:
- \(3x^3 \cdot (-4x^3) = -12x^{6}\)
- \(3x^3 \cdot 5 = 15x^{3}\)
Now, combining these results gives:
\[ A = -12x^6 + 15x^3 \]
Thus, the area of the rectangle is
\(-12x^6 + 15x^3\).
So the correct answer is:
−12x^6 + 15x^3