Question

Find the area of the rectangle below:

3x3

−4x3 +5

(1 point)
Responses

−12x9+15x3
negative 12 x to the 9th power plus 15 x cubed

11x3−2
11 x cubed minus 2

−12x6+15x3
negative 12 x to the 6th power plus 15 x cubed

12x6−15x3
12 x to the 6th power minus 15 x cubed

−x3+5

Answer 1

To find the area of the rectangle, we need to multiply the two given expressions:

1. The first expression is \(3x^3\).
2. The second expression is \(-4x^3 + 5\).

The area \(A\) can be calculated as follows:

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

Now we can use the distributive property to expand this expression:

\[
A = 3x^3 \cdot (-4x^3) + 3x^3 \cdot 5
\]

Calculating each term:

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

Now, we can combine these results:

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

Therefore, the area of the rectangle is:

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

This matches with one of the responses provided: "−12x6 + 15x3".