Question

Find the area of the rectangle: On the side of the rectangle, it shows: 3x^3. On the bottom of the rectangle, it shows: -4x^3 + 5

Answer 1

To find the area of a rectangle, you multiply the length and the width. In this case, we have:

- Length = \( 3x^3 \)
- Width = \( -4x^3 + 5 \)

The area \( A \) of the rectangle can be calculated using the formula:

\[
A = \text{Length} \times \text{Width}
\]

Substituting the given dimensions:

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

Now, we will distribute \( 3x^3 \) to each term in the parentheses:

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

Calculating each term separately:

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

Now, we can combine these results:

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

Thus, the area of the rectangle is:

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