Question

suppose a large cubic box mesuring 3 feet on each side contains a smaller cubic box that mesurs x feeton each side write a polynomial that repersents the volume of each emty space left in the large bo

Answer 1

Sure, let's proceed step by step!

Step 1: Calculating the Volume of the Large Cube
The volume of a cube is calculated by cubing the side length. Therefore, for our large cube that measures 3 feet on each side, we cube 3 to find its volume: 3^3 = 27 cubic feet.

Step 2: Representing the Volume of the Smaller Cube as a Polynomial
Similarly, the volume of the smaller cube is calculated by cubing its side length (which is x feet). So, the volume of the smaller cube is represented by the polynomial x^3.

Step 3: Calculating the Empty Space in the Large Cube
The empty space is the volume of the large cube that is not filled by the smaller cube. We calculate this by subtracting the volume of the smaller cube from the volume of the large cube. This gives us: 27 - x^3.

So, the polynomial that represents the volume of empty space left in the large cube is 27 - x^3. This means that for any given side length x of the smaller cube, we can calculate the amount of cubic feet of empty space in the large cube.