Question

The dimensions of a box are x, 2x, and 3x. Each dimension is increased by 3. Calculate the volume of the box.

Answer 1

The volume of the box would be 6x³+33x²+54x+27.

Explanation:

The new dimensions of the box would be (x+3), (2x+3), and (3x+3). Since the volume of a rectangular prism are calculated by multiplying the length, width, and depth, we can just multiply all three of these dimensions together to come up with the answer.

Using foil on the first two terms originally you get (x+3)×(2x+3)= 2x²+3x+6x+9 which can be simplified to 2x²+9x+9.

Then you multiply this equation by (3x+3). (2x²+9x+9)×(3x+3)= 6x³+6x²+27x²+27x+27x+27 which can be simplified to 6x³+33x²+54x+27.

Answer 2

6x³+33x²+54x+27

Explanation:

dimensions are now:

x+3, 2x+3, 3x+3

Volume

• V=lwh
• V= (x+3)(2x+3)(3x+3)=
• 3(x+1)(x+3)(2x+3)=
• 3( x² + 4x+3)(2x+3)=
• 3(2x³+11x²+18x+9)=
• 6x³+33x²+54x+27