Question

A box is created from a regular piece of cardboard 18 centimeters by 24 centimeters by cutting a square from each corner and folding up the sides, as shown for the diagram. Write an expression for the volume of the box as a polynomial in standard form.

Answer 1

Answer:    4x^3 - 84x^2 + 432x

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Explanation:

The horizontal side 24 drops to 24-2x after we subtract off two copies of x (left and right). Similarly, the 18 drops to 18-2x.

The box has dimensions of:

• 24-2x
• 18-2x
• x

Multiply out those dimensions to get the volume

Volume = Length*Width*Height

V = L*W*H

V = (24-2x)(18-2x)x

V = x(24-2x)(18-2x)

V = x(432 - 48x - 36x + 4x^2)

V = x(4x^2 - 84x + 432)

V = 4x^3 - 84x^2 + 432x

Side note: x > 0