Question

what is the area of a rectangle if the width is 3x^3 and the length is -4x^3 + 5

Answer 1

To find the area of a rectangle, you multiply the width by the length. Given that the width is \( 3x^3 \) and the length is \( -4x^3 + 5 \), we can calculate the area \( A \) as follows:

\[
A = \text{width} \times \text{length} = (3x^3)(-4x^3 + 5)
\]

Now, we can distribute the \( 3x^3 \):

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

Calculating each term separately:

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

Combining both terms gives:

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

Thus, the area of the rectangle is:

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