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

1 answer

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) \(-12x^6 + 15x^3\).