Question

The length in meters of a cardboard box is represented by the expression 5x - 12. The width in meters of the cardboard box is represented by the expression 3x + 7. The height of the cardboard box is 3x meters. What simplified expression represents the capacity that the cardboard box could hold?

Answer 1

The simplified expression for the volume of a cardboard box with the given dimensions (5x - 12) for length, (3x + 7) for width, and (3x) for height is 45x^3 - 3x^2 - 252x cubic meters.

Step-by-step explanation:

The student is asking for the simplified expression that represents the volume or capacity of a cardboard box. Given that the length, width, and height of the box are represented by the expressions 5x - 12, 3x + 7, and 3x respectively, the volume can be found by multiplying these expressions together.

The calculation would be as follows:

• Volume = Length × Width × Height
• Volume = (5x - 12) × (3x + 7) × 3x

To find the simplified expression, we need to perform the multiplication:

1. Multiply the expressions for length and width: (5x - 12)(3x + 7).
2. This gives us a quadratic expression: 15x2 + 35x - 36x - 84.
3. Simplify the quadratic expression: 15x2 - x - 84.
4. Multiply the result by the height: (15x2 - x - 84) × 3x.
5. This yields the simplified expression for volume: 45x3 - 3x2 - 252x.

Therefore, the capacity of the cardboard box, in cubic meters, is represented by the simplified expression 45x3 - 3x2 - 252x.