Question

Find the area of the rectangle below:

right side is 3x^3

bottom side is -4x^3 + 5

(1 point)
Responses

12x6−15x3

−12x9+15x3

−12x6+15x3

−x^3+5

11x^3−2

Answer 1

To find the area of the rectangle, we need to multiply the lengths of its sides.

The right side of the rectangle is given as \(3x^3\) and the bottom side is given as \(-4x^3 + 5\).

Now, we will calculate the area (A):

\[
A = \text{Right Side} \times \text{Bottom Side} = (3x^3) \times (-4x^3 + 5)
\]

To calculate this, we distribute \(3x^3\) to both terms in the expression for the bottom side:

\[
A = 3x^3 \times -4x^3 + 3x^3 \times 5
\]

Calculating each part, we get:

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

Now, we can combine these results to find the total area:

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

Therefore, the area of the rectangle is:

\[
\boxed{-12x^6 + 15x^3}
\]

This corresponds to the third option in the responses provided.