Find the area of the rectangle below:

Question

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

Answer 1

To find the area of the rectangle given the expressions \(3x^3\) and \(-4x^3 + 5\), we need to multiply these two expressions together:

\[ \text{Area} = (3x^3)(-4x^3 + 5) \]

Now, we will distribute \(3x^3\) to both terms in the second expression:

\[ \text{Area} = 3x^3 \cdot (-4x^3) + 3x^3 \cdot 5 \]

Calculating each part:

1. \(3x^3 \cdot (-4x^3) = -12x^{3 + 3} = -12x^6\)
2. \(3x^3 \cdot 5 = 15x^3\)

Now combine these results:

\[ \text{Area} = -12x^6 + 15x^3 \]

Thus, the area of the rectangle is:

\[ -12x^6 + 15x^3 \]

From the options provided, the correct response is:

−12x^6 + 15x^3.