A cube is shrunk so that its side lengths of 2x are reduced by 3 units. Using the Binomial Theorem, which of the following is the correct expression for the new volume of the cube?(1 point)

8x^3−36x^2+54x+27

8x^3+36x^2+54x−27

8x^3−36x^2+54x−27

8x^3+36x^2+54x+27

1 answer

The correct expression for the new volume of the cube can be determined by expanding the expression for the volume of the original cube, and then substituting (2x - 3) for each side length.

The original volume of the cube is given by (2x)^3 = 8x^3.

Substituting (2x - 3) for each side length, we get:
(2x - 3)(2x - 3)(2x - 3) = (2x - 3)^3

Using the Binomial Theorem, this expression expands to:
8x^3 - 36x^2 + 54x - 27.

Therefore, the correct expression for the new volume of the cube is:
8x^3 - 36x^2 + 54x - 27.

So, the correct answer is: 8x^3 - 36x^2 + 54x - 27.