Question

 Find the area of the rectangle below: 3x^3, -4x^3 + 5
A) 12x^6 - 15x^3
B) -12x^9 + 15x^3
C) -12x^6 + 15x^3
D) -x^3 + 5
E) 11x^3 - 2

Answer 1

To find the area of a rectangle, we multiply its length and width. Here, the expressions for the sides of the rectangle are \( 3x^3 \) and \( -4x^3 + 5 \).

Let's calculate the area:

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

Now, distribute \( 3x^3 \) across the two terms in the second expression:

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

Calculating each term separately:

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

Now, combine these results:

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

So, the area of the rectangle is

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

The answer is option **C)** \(-12x^6 + 15x^3\).