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 \(-4x^3 + 5\):
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Multiply \(3x^3\) by \(-4x^3\): \[ 3x^3 \times -4x^3 = -12x^{3+3} = -12x^6 \]
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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